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[]
[null,null,null,null,"Forward",null,null,null,null,null,null,null,null,null,"Contents"]
[]
[]
[null,null,null,null,"This Workbook offers a collection of standard statistical tests in a manner that is intended to be easily accessible from the desktop.\n\nFree of charge by the Stats People Ltd.\n\n\n",null,null,null,null,null,null,null,null,null,null,{"$f":" contents","v":"1         HYPOTHESIS TESTS FOR PROPORTIONS"}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"1.1       Proportion vs Hypothesised"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"1.2       Proportion: Total vs Subset"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"1.3       Two Proportion: Independent Samples"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"1.4       Two Proportions: Same Sample, Mutually Exclusive"]
[null,null,null,null,"      Lead author\n\n\n\n\n",null,null,null,null,null,null,null,null,null,null,"1.5       Two Proportions: Same Sample, Overlapping"]
[null,null,null,null,"            Gary Bennett\n\n\n",null,null,null,null,null,null,null,null,null,null,"2         HYPOTHESIS  TESTS FOR MEANS"]
[null,null,null,null,"      Co-authored by\n\n\n\n",null,null,null,null,null,null,null,null,null,null,"2.1       Mean vs Hypothesised"]
[null,"Use the tabs above",null,null,"            Sarah Venables\n\n\n\n",null,null,null,null,null,null,null,null,null,null,"2.2       Two Means: Independent Samples"]
[null,"to navigate first to",null,null,"            Hon-Kit Choy\n",null,null,null,null,null,null,null,null,null,null,"2.3       Two Means: Same Samples (Repeated Measures)"]
[null,"section head pages",null,null,"            Jack O'Donnell\n\n\n\n",null,null,null,null,null,null,null,null,null,null,"3         CONFIDENCE INTERVALS FOR PROPORTIONS"]
[null,"and then onward ",null,null,"      Graphic design and Excel™ implementation\n\n\n\n",null,null,null,null,null,null,null,null,null,null,"3.1      Proportion using Normal Confidence Interval"]
[null,"to the tests.",null,null,"            Peter Bartholomew\n\n\n",null,null,null,null,null,null,null,null,null,null,"3.2      Proportion using Wilson's Confidence Interval"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"3.3       Proportion: Total vs Subset"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"3.4       Two Proportion: Independent Samples"]
[null,null,null,null,"Copyright\n\n\n\n",null,null,null,null,null,null,null,null,null,null,"3.5       Two Proportions: Same Sample, Mutually Exclusive"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"3.6       Two Proportions: Same Sample, Overlapping"]
[null,null,null,null,"     © The Stats People Ltd.  2023\n\n\n\n",null,null,null,null,null,null,null,null,null,null,"4         CONFIDENCE INTERVALS FOR MEANS"]
[null,null,null,null,"      http://www.statspeople.com/",null,null,null,null,null,null,null,null,null,null,"4.1       Mean vs Hypothesised"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"4.2       Two Means: Independent Samples (Unequal Variance)"]
[null,null,null,null,"Version 3.1",null,null,null,null,null,null,null,null,null,null,"4.3       Two Means: Same Samples (Repeated Measures)"]
[]
[null,null,null,null,"Whilst this spreadsheet has been carefully written and subject to peer group review, it is the user's responsibility to check that the assumptions and results obtained from the workbook are correct.  Neither the StatsPeople nor the authors can accept any liability for incorrect results. \n\nThe Stats People Ltd\nTrading Address: Unit 3, 7 Blighs Walk, Sevenoaks, Kent TN13 1DB;  \nRegistered Address: 19-21 Swan Street, West Malling, Kent ME19 6JU;  \nCompany. No: 9828882 in England and Wales."]

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[]
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[null,null,null,null,"Notes",null,null,null,null,null,null,null,null,null,"Contents Section 1 "]
[]
[null,null,null,null,"This section offers a number of tests used for determining the significance of estimates of proportion taken from a sample"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,1,{"$f":" S1.tests","v":"Sample vs Hypothesised"}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2,"Total vs Subset"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,3,"Independent Samples"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,4,"Same Sample, Mutually Exclusive"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,5,"Same Sample, Overlapping"]

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[null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"RefValues!Q16","v":"Sample vs Hypothesised"}]
[]
[]
[]
[]
[]
[]
[null,null,null,null,"Notes",null,null,null,null,null,null,null,null,null,"Input",null,null,null,null,null,"Confidence level"]
[]
[null,null,null,null,"This tests the Null hypothesis that a proportion estimated in a sample is equal to some hypothesised population proportion.  Type the relevant values into the cells in the INPUT section and set the desired level of confidence. A significant (low) p-value suggests that we should reject the Null Hypothesis and that the difference between two proportions is statistically significant.",null,null,null,null,null,null,null,null,null,null,null,"Percentage hypothesis:",null,"p₀%",null,null,2]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Percentage sample:",null,"p̂%"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sample size",null,"n"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"critical value",{"$f":" _xlfn.NORM.S.INV( 1 - INDEX(level,level.index)/100/2 )","v":1.9599639845400536}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":" IF(incomplete?,\"Please complete data entry\",IF(nonNumeric?,\"All input values must be numbers\",\"\"))","v":"Please complete data entry"}]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND(size.invalid?,NOT(incomplete?)),\"RESPONDENT NUMBERS MUST BE GREATER THAN ZERO!!\",\"\")","v":""}]
[]
[null,null,null,null,"The test statistic is     "]
[]
[]
[]
[null,null,null,null,"where  "]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Result"]
[null,null,null,null,"Z    =","  Z statistic"]
[null,null,null,null,"p₀  =","  Hypothesis sample proportion"]
[null,null,null,null,"p̂   =","  Sample Proportion"]
[null,null,null,null,"n   =","  Sample size",null,null,null,null,null,null,null,null,null,"Difference: ",{"$f":"IF( OK?, 100 * (p̂ - p₀), IF(incomplete?,\"\",\"WHOOPS!\") )","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Standard Error: ",{"$f":" IF( OK?, 100 * SQRT( p₀*(1-p₀)/n ), \"\" )","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Test statistic Z: ",{"$f":" IF( OK?, Δ / ᶓ, \"\" )","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"p-value: ",{"$f":" IF( OK?, 2 * (1 - _xlfn.NORM.S.DIST( ABS(Z),TRUE) ), \"\" )","v":""}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Outcome: ",{"$f":" IF( OK?,\n           IF( ABS(Z) > Z‡,\n                \"SIGNIFICANT DIFFERENCE!\",\n                \"Difference not significant\")\n           & \" (at the \"& (level.selected) &\"% level)\",\n    \"\" )","v":""}]

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[]
[]
[]
[]
[]
[]
[null,null,null,null,"Notes",null,null,null,null,null,null,null,null,null,"Input",null,null,null,null,null,"Level setting"]
[]
[null,null,null,null,"This test is used for comparing proportions estimated in a subset of a sample against the total sample.  It tests the Null hypothesis that the population proportions in the total and subset are equal.  Type  the  relevant  values into the cells in the  INPUT  section and set the desired level of confidence.  A significant (low) p-value suggests that we should reject the Null Hypothesis and that the difference between two proportions is statistically significant.      ",null,null,null,null,null,null,null,null,null,null,null,"Percentage for total:",null,"Ρ̂%",null,null,1]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Percentage for sub-group:",null,"p̂%"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Total respondents (base):",null,"Ν"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Number in sub-group (base):",null,"n",null,"critical value",{"$f":" _xlfn.NORM.S.INV( 1 - INDEX(level,level.index)/100/2 )","v":2.5758293035488999}]
[]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND(NOT(incomplete?),size.invalid?),\"RESPONDENT NUMBERS MUST BE > 0 AND THE SUB-GROUP SHOULD BE SMALLER!!\",\"\")","v":""}]
[]
[null,null,null,null,"The test statistic is     "]
[]
[]
[]
[null,null,null,null,"where  "]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Result"]
[null,null,null,null,"Z  ="," Z statistic"]
[null,null,null,null,"P̂  ="," Sample Proportion for Total"]
[null,null,null,null,"p̂  ="," Sample Proportion for Subset"]
[null,null,null,null,"N  ="," Total sample size",null,null,null,null,null,null,null,null,null,"Difference: ",{"$f":"IF( OK?, 100 * ( p̂ - Ρ̂ ), IF(incomplete?,\"\",\"WHOOPS!\") )","v":""}]
[null,null,null,null,"n  ="," Subgroup sample size",null,null,null,null,null,null,null,null,null,"Standard Error: ",{"$f":" IF( OK?, 100 * SQRT( Ρ̂*(1-Ρ̂)/n * (Ν-n)/Ν ), \"\" )","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Test statistic Z: ",{"$f":" IF( OK?, Δ / ᶓ, \"\" )","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"p-value: ",{"$f":" IF( OK?, 2 * (1 - _xlfn.NORM.S.DIST( ABS(Z),TRUE) ), \"\" )","v":""}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Outcome: ",{"$f":" IF( OK?,\n           IF( ABS(Z) > Z‡,\n                \"SIGNIFICANT DIFFERENCE!\",\n                \"Difference not significant\")\n           & \" (at the \"& level.selected &\"% level)\",\n    \"\" )","v":""}]

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[null,null,null,null,"Notes",null,null,null,null,null,null,null,null,null,"Input",null,null,null,null,null,"Level setting"]
[]
[null,null,null,null,"This test is used for comparing proportions estimated in two Independent samples. It tests the Null hypothesis that the proportion in both populations is the same. Type the relevant values into the cells in the INPUT section and set the desired level of confidence.  A significant (low) p-value suggests that we should reject the Null Hypothesis and that the difference between two proportions is statistically significant.  This version of the test assumes that population variances for each subgroup are the same.",null,null,null,null,null,null,null,null,null,null,null,"Sample proportion from subgroup 1:",null,"p̂₁%",null,null,2]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sample proportion from subgroup 2:",null,"p̂₂%"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sample size of subgroup 1:",null,"n₁"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sample size of subgroup 2:",null,"n₂",null,"critical value",{"$f":" _xlfn.NORM.S.INV( 1 - INDEX(level,level.index)/100/2 )","v":1.9599639845400536}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Proportion (normalisation):",{"$f":" IF( OK?, 100 * ( p̂₁*n₁ + p̂₂*n₂) / ( n₁ + n₂), \"\" )","v":""},"p̂ %"]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":" IF(incomplete?,\"Please complete data entry\",IF(nonNumeric?,\"All input values must be numbers\",\"\"))","v":"Please complete data entry"},null,null,null,null,"Variance"]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":" IF(AND(size.invalid?,NOT(incomplete?)),\"RESPONDENT NUMBERS MUST BE GREATER THAN ZERO!!\",\"\")","v":""}]
[null,null,null,null,"The test statistic is     "]
[]
[]
[]
[null,null,null,null,"where  "]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Result"]
[null,null,null,null,"and"]
[]
[null,null,null,null,"Z   ="," Z statistic"]
[null,null,null,null,"p̂₁  ="," Sample Proportion from subgroup 1",null,null,null,null,null,null,null,null,null,"Difference: ",{"$f":"IF( OK?, 100 * (p̂₁ - p̂₂), IF(incomplete?,\"\",\"WHOOPS!\") )","v":""}]
[null,null,null,null,"p̂₂  ="," Sample Proportion from subgroup 2",null,null,null,null,null,null,null,null,null,"Standard Error: ",{"$f":" IF( OK?, 100 * SQRT( p̂*(1-p̂) * (1/n₁ + 1/n₂) ), \"\" )","v":""}]
[null,null,null,null,"n₁  ="," Sample size of subgroup 1",null,null,null,null,null,null,null,null,null,"Test statistic Z: ",{"$f":" IF( OK?, Δ / ᶓ, \"\" )","v":""}]
[null,null,null,null,"n₂  ="," Sample size of subgroup 2",null,null,null,null,null,null,null,null,null,"p-value: ",{"$f":" IF( OK?, 2 * (1 - _xlfn.NORM.S.DIST( ABS(Z),TRUE) ), \"\" )","v":""}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Outcome: ",{"$f":" IF( OK?,\n           IF( ABS(Z) > Z‡,\n                \"SIGNIFICANT DIFFERENCE!\",\n                \"Difference not significant\")\n           & \" (at the \"& level.selected &\"% level)\",\n    \"\" )","v":""}]

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[]
[]
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[]
[null,null,null,null,"Notes",null,null,null,null,null,null,null,null,null,"Input",null,null,null,null,null,"Level setting"]
[]
[null,null,null,null,"This test is used for comparing proportions estimated in two Independent samples. It tests the Null hypothesis that the proportion in both populations is the same. Type the relevant values into the cells in the INPUT section and set the desired level of confidence.  A significant (low) p-value suggests that we should reject the Null Hypothesis and that the difference between two proportions is statistically significant.  This version of the test assumes that population variances for each subgroup are different.",null,null,null,null,null,null,null,null,null,null,null,"Sample proportion from subgroup 1:",null,"p̂₁%",null,null,2]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sample proportion from subgroup 2:",null,"p̂₂%"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sample size of subgroup 1:",null,"n₁"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sample size of subgroup 2:",null,"n₂",null,"critical value",{"$f":" _xlfn.NORM.S.INV( 1 - INDEX(level,level.index)/100/2 )","v":1.9599639845400536}]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":" IF(incomplete?,\"Please complete data entry\",IF(nonNumeric?,\"All input values must be numbers\",\"\"))","v":"Please complete data entry"},null,null,null,null,"Variance"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(percent.invalid?,\"PERCENTAGES MUST BE BETWEEN 0 AND 100!\", \"\" )","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":" IF(AND(size.invalid?,NOT(incomplete?)),\"RESPONDENT NUMBERS MUST BE GREATER THAN ZERO!!\",\"\")","v":""}]
[null,null,null,null,"The test statistic is     "]
[]
[]
[]
[null,null,null,null,"where  "]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Result"]
[]
[]
[null,null,null,null,"Z   ="," Z statistic"]
[null,null,null,null,"p̂₁  ="," Sample Proportion from subgroup 1",null,null,null,null,null,null,null,null,null,"Difference: ",{"$f":"IF( OK?, 100 * (p̂₁ - p̂₂), IF(incomplete?,\"\",\"WHOOPS!\") )","v":""}]
[null,null,null,null,"p̂₂  ="," Sample Proportion from subgroup 2",null,null,null,null,null,null,null,null,null,"Standard Error: ",{"$f":" IF( OK?, 100 * SQRT( p̂₁*(1-p̂₁)/n₁ + p̂₂*(1-p̂₂)/n₂ ), \"\" )","v":""}]
[null,null,null,null,"n₁  ="," Sample size of subgroup 1",null,null,null,null,null,null,null,null,null,"Test statistic Z: ",{"$f":" IF( OK?, Δ / ᶓ, \"\" )","v":""}]
[null,null,null,null,"n₂  ="," Sample size of subgroup 2",null,null,null,null,null,null,null,null,null,"p-value: ",{"$f":" IF( OK?, 2 * (1 - _xlfn.NORM.S.DIST( ABS(Z),TRUE) ), \"\" )","v":""}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Outcome: ",{"$f":" IF( OK?,\n           IF( ABS(Z) > Z‡,\n                \"SIGNIFICANT DIFFERENCE!\",\n                \"Difference not significant\")\n           & \" (at the \"& level.selected &\"% level)\",\n    \"\" )","v":""}]

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[]
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[]
[null,null,null,null,"Notes",null,null,null,null,null,null,null,null,null,"Input",null,null,null,null,null,"Level setting"]
[]
[null,null,null,null,"This test is used for comparing two mutually exclusive (Single-coded) proportions (e.g. Very Satisfied and Very Dissatisfied) in the same sample. It tests the Null hypothesis that the two proportions are equal in the population. Type the relevant values into the cells in the INPUT section and set the desired level of confidence.  A significant (low) p-value suggests that we should reject the Null Hypothesis and that the difference between two proportions is statistically significant.",null,null,null,null,null,null,null,null,null,null,null," Sample Proportion in A:",null,"p̂ₐ%",null,null,3]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null," Sample Proportion in B:",null,"p̂ᵦ%"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sample size:",null,"n"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"critical value",{"$f":" _xlfn.NORM.S.INV( 1 - INDEX(level,level.index)/100/2 )","v":1.6448536269514715}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":" IF(incomplete?,\"Please complete data entry\",IF(nonNumeric?,\"All input values must be numbers\",\"\"))","v":"Please complete data entry"}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(percent.invalid?,\"PERCENTAGES MUST BE BETWEEN 0 AND 100 AND TOTAL A MAXIMUM OF 100%!\", \"\" )","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND(size.invalid?,NOT(incomplete?)),\"RESPONDENT NUMBERS MUST BE GREATER THAN ONE!!\",\"\")","v":""}]
[]
[null,null,null,null,"The test statistic is     "]
[]
[]
[]
[null,null,null,null,"where  "]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Result"]
[null,null,null,null,"Z   ="," Z statistic"]
[null,null,null,null,"p̂ₐ  ="," Sample Proportion in A"]
[null,null,null,null,"p̂ᵦ  ="," Sample Proportion in B"]
[null,null,null,null,"n   ="," Sample Size",null,null,null,null,null,null,null,null,null,"Difference: ",{"$f":"IF( OK?, 100 * (p̂ₐ - p̂ᵦ), IF(incomplete?,\"\",\"WHOOPS!\") )","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Standard Error: ",{"$f":" IF( OK?, 100 * SQRT( (p̂ₐ*(1-p̂ₐ) +  p̂ᵦ*(1- p̂ᵦ) + 2*p̂ₐ*p̂ᵦ ) / (n - 1) ), \"\" )","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Test statistic Z: ",{"$f":" IF( OK?, Δ / ᶓ, \"\" )","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"p-value: ",{"$f":" IF( OK?, 2 * (1 - _xlfn.NORM.S.DIST( ABS(Z),TRUE) ), \"\" )","v":""}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Outcome: ",{"$f":" IF( OK?,\n           IF(ABS(Z)>Z‡,\n                \"SIGNIFICANT DIFFERENCE!\",\n                \"Difference not significant\")\n           & \" (at the \"& level.selected &\"% level)\",\n    \"\" )","v":""}]

{"sheet":"S1test5","index":7,"n_rows":35,"n_cols":22,"rows_kept":35,"cut":false,"hidden":false,"merged":[[11,4,18,10]]}
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"RefValues!Q20","v":"Same Sample, Overlapping"}]
[]
[]
[]
[]
[]
[]
[null,null,null,null,"Notes",null,null,null,null,null,null,null,null,null,"Input",null,null,null,null,null,"Level setting"]
[]
[null,null,null,null,"This test is used for comparing two overlapping (multi-coded) proportions in the same sample (e.g. Awareness of Brand X and Brand Y). It tests the Null hypothesis that the two proportions are equal in the population. Type the relevant values into the cells in the INPUT section and set the desired level of confidence.  A significant (low) p-value suggests that we should reject the Null Hypothesis and that the difference between two proportions is statistically significant.",null,null,null,null,null,null,null,null,null,null,null,"Sample percentage in A:",null,"p̂ₐ%",null,null,2]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sample percentage in B:",null,"p̂ᵦ%"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null," Sample percentage in A AND B",null,"p̂ₐᵦ%"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sample size:",null,"n",null,"critical value",{"$f":" _xlfn.NORM.S.INV( 1 - INDEX(level,level.index)/100/2 )","v":1.9599639845400536}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":" IF(incomplete?,\"Please complete data entry\",IF(nonNumeric?,\"All input values must be numbers\",\"\"))","v":"Please complete data entry"}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(percent.invalid?,\n       \"PERCENTAGES MUST BE BETWEEN 0 AND 100!\",\n         IF( p̂ₐᵦ > MIN(p̂ₐ,p̂ᵦ),\n              \"p̂ₐᵦ cannot be greater than p̂ₐ or p̂ᵦ\",\n               \"\" )\n          )","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND(size.invalid?,NOT(incomplete?)),\"RESPONDENT NUMBERS MUST BE GREATER THAN ONE!!\",\"\")","v":""}]
[]
[null,null,null,null,"The test statistic is     "]
[]
[]
[]
[null,null,null,null,"where  "]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Result"]
[null,null,null,null,"Z   ="," Z statistic"]
[null,null,null,null,"p̂ₐ  ="," Sample Proportion in A"]
[null,null,null,null,"p̂ᵦ  ="," Sample Proportion in B"]
[null,null,null,null,"p̂ₐᵦ ="," Sample Proportion in A AND B",null,null,null,null,null,null,null,null,null,"Difference: ",{"$f":" IF(incomplete?,\"\",IF(nonNumeric?,\"WHOOPS!\",IF(OK?, 100 * (p̂ₐ - p̂ᵦ),\"WHOOPS!\") ))","v":""}]
[null,null,null,null,"n   ="," Sample Size",null,null,null,null,null,null,null,null,null,"Standard Error: ",{"$f":" IF(nonNumeric?,\"\",IF( OK?, 100 * SQRT( ( p̂ₐ* (1-p̂ₐ) +  p̂ᵦ* (1- p̂ᵦ) + 2 * ( p̂ₐ* p̂ᵦ - p̂ₐᵦ ) ) / (n - 1) ), \"\" ))","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Test statistic Z: ",{"$f":" IF(nonNumeric?,\"\", IF( OK?, Δ / ᶓ, \"\" ))","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"p-value: ",{"$f":" IF(nonNumeric?,\"\", IF( OK?, 2 * (1 - _xlfn.NORM.S.DIST( ABS(Z),TRUE) ), \"\" ))","v":""}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Outcome: ",{"$f":" IF(nonNumeric?,\"\", IF( OK?,\n           IF( ABS(Z) > Z‡,\n                \"SIGNIFICANT DIFFERENCE!\",\n                \"Difference not significant\")\n           & \" (at the \"& level.selected &\"% level)\",\n    \"\" ))","v":""}]

{"sheet":"Section2","index":8,"n_rows":15,"n_cols":16,"rows_kept":15,"cut":false,"hidden":false,"merged":[[11,4,28,10]]}
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"RefValues!Q21","v":"HYPOTHESIS  TESTS FOR MEANS"}]
[]
[]
[]
[]
[]
[]
[null,null,null,null,"Notes",null,null,null,null,null,null,null,null,null,"Contents Section 2"]
[]
[null,null,null,null,"This section offers a number of tests used for determining the significance of estimates of population means taken from a sample"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,1,{"$f":" S2.tests","v":"Mean vs Hypothesised"}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2,"Independent Samples"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,3,"Same Samples (Repeated Measures)"]

{"sheet":"S2test1","index":9,"n_rows":36,"n_cols":22,"rows_kept":36,"cut":false,"hidden":false,"merged":[[11,4,17,10]]}
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"RefValues!Q22","v":"Mean vs Hypothesised"}]
[]
[]
[]
[]
[]
[]
[null,null,null,null,"Notes",null,null,null,null,null,null,null,null,null,"Input",null,null,null,null,null,"Confidence level"]
[]
[null,null,null,null,"This tests the Null hypothesis that a mean statistic estimated in a sample is equal to some hypothesised population mean.  Type the relevant values into the cells in the INPUT section and set the desired level of confidence. A significant (low) p-value suggests that we should reject the Null Hypothesis and that the difference between two means is statistically significant. ",null,null,null,null,null,null,null,null,null,null,null,"Sample mean",null,"x̅",null,null,3]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Hypothesised population mean",null,"μ₀"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sample standard deviation",null,"s"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sample size",null,"n",null,"critical value",{"$f":" IF( OK?, _xlfn.T.INV.2T( INDEX(level,level.index)/100, d.f. ), \"\" )","v":""}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":" IF(incomplete?,\"Please complete data entry\",IF(nonNumeric?,\"All input values must be numbers\",\"\"))","v":"Please complete data entry"}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND(NOT(incomplete?),stdDev.invalid?),\"STANDARD DEVIATIONS MUST BE GREATER THAN ZERO!\", \"\" )","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND(size.invalid?,NOT(incomplete?)),\"RESPONDENT NUMBERS MUST BE GREATER THAN ONE!!\",\"\")","v":""}]
[]
[null,null,null,null,"The test statistic is     "]
[]
[]
[]
[null,null,null,null,"where  "]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Result"]
[null,null,null,null,"t    =","  t statistic"]
[null,null,null,null,"x̅    =","  Sample Mean"]
[null,null,null,null,"μ₀  =","  Hypothesised Population Mean"]
[null,null,null,null,"s    =","  Sample Standard Deviation",null,null,null,null,null,null,null,null,null,"Difference: ",{"$f":"IF( OK?, (x̅ - μ₀), IF(incomplete?,\"\",\"WHOOPS!\") )","v":""}]
[null,null,null,null,"n    =","  Sample size",null,null,null,null,null,null,null,null,null,"Standard error: ",{"$f":" IF( OK?, s / √n, \"\" )","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Test statistic, t: ",{"$f":" IF( OK?, Δ / ᶓ, \"\" )","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"d.f. : ",{"$f":" IF( OK?, n - 1, \"\" )","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"p-value: ",{"$f":" IF( OK?, _xlfn.T.DIST.2T( ABS(t), d.f.), \"\" )","v":""}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Outcome: ",{"$f":" IF( OK?,\n           IF( ABS(t) > t‡,\n                \"SIGNIFICANT DIFFERENCE!\",\n                \"Difference not significant\")\n           & \" (at the \"& (level.selected) &\"% level)\",\n    \"\" )","v":""}]

{"sheet":"S2test2a","index":10,"n_rows":36,"n_cols":22,"rows_kept":36,"cut":false,"hidden":false,"merged":[[11,4,18,10]]}
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"RefValues!Q23  & \"  (\" & RefValues!U23 & \")\"","v":"Independent Samples  (Equal Variance)"}]
[]
[]
[]
[]
[]
[]
[null,null,null,null,"Notes",null,null,null,null,null,null,null,null,null,"Input",null,null,null,null,null,"Confidence level"]
[]
[null,null,null,null,"This test is used for comparing mean statistics estimated in two Independent samples. It tests the Null hypothesis that the mean in both populations is the same. Type the relevant values into the cells in the INPUT section and set the desired level of confidence.  A significant (low) p-value suggests that we should reject the Null Hypothesis and that the difference between two means is statistically significant. This version of the test assumes that population variances for each subgroup are the same.",null,null,null,null,null,null,null,null,null,null,null,"Sample 1","Sample 2",null,null,null,3]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Means",null,null,"x̅ᵣ"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Standard deviation",null,null,"sᵣ"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Size",null,null,"nᵣ",null,"critical value",{"$f":" IF( OK?, _xlfn.T.INV.2T( INDEX(level,level.index)/100, d.f. ), \"\" )","v":""}]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":" IF(incomplete?,\"Please complete data entry\",IF(nonNumeric?,\"All input values must be numbers\",\"\"))","v":"Please complete data entry"},null,null,null,null,"Variance"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF( AND(stddev.invalid?, NOT(incomplete?)),\"STANDARD DEVIATIONS  MUST BE GREATER THAN ZERO !\", \"\" )","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND(size.invalid?,NOT(incomplete?)), \"SAMPLE NUMBERS MUST BE GREATER THAN ONE!!\",\"\")","v":""}]
[null,null,null,null,"The test statistic is     "]
[]
[]
[]
[null,null,null,null,"where  "]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Result"]
[]
[null,null,null,null,"and"]
[null,null,null,null,"t     =","  t statistic"]
[null,null,null,null,"x̅₁   =","  Sample 1 Mean",null,null,null,null,null,null,null,null,null,"Difference: ",{"$f":"IF( OK?, (x̅₁ - x̅₂), IF(incomplete?,\"\",\"WHOOPS!\") )","v":""}]
[null,null,null,null,"x̅₂   =","  Sample 2 Mean",null,null,null,null,null,null,null,null,null,"Standard error: ",{"$f":" IF( OK?, SQRT( ( (n₁-1)*s₁² + (n₂-1)*s₂² ) / (n₁ + n₂ - 2) * ( 1/n₁ + 1/n₂) ), \"\" )","v":""}]
[null,null,null,null,"s₁    =","  Sample 1 Standard deviation",null,null,null,null,null,null,null,null,null,"Test statistic, t: ",{"$f":" IF( OK?, Δ / ᶓ, \"\" )","v":""}]
[null,null,null,null,"s₂    =","  Sample 2 Standard deviation",null,null,null,null,null,null,null,null,null,"d.f. : ",{"$f":" IF( OK?, n₁ + n₂ - 2, \"\" )","v":""}]
[null,null,null,null,"n₁   =","  Sample 1 size",null,null,null,null,null,null,null,null,null,"p-value: ",{"$f":" IF( OK?, _xlfn.T.DIST.2T( ABS(t), d.f.), \"\" )","v":""}]
[null,null,null,null,"n₂   =","  Sample 2 size"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Outcome: ",{"$f":" IF( OK?,\n           IF( ABS(t) > t‡,\n                \"SIGNIFICANT DIFFERENCE!\",\n                \"Difference not significant\")\n           & \" (at the \"& (level.selected) &\"% level)\",\n    \"\" )","v":""}]

{"sheet":"S2test2b","index":11,"n_rows":36,"n_cols":22,"rows_kept":36,"cut":false,"hidden":false,"merged":[[11,4,18,10]]}
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"RefValues!Q23  & \"  (\" & RefValues!X23 & \")\"","v":"Independent Samples  (Different Variance)"}]
[]
[]
[]
[]
[]
[]
[null,null,null,null,"Notes",null,null,null,null,null,null,null,null,null,"Input",null,null,null,null,null,"Confidence level"]
[]
[null,null,null,null,"This test is used for comparing mean statistics estimated in two Independent samples. It tests the Null hypothesis that the mean in both populations is the same. Type the relevant values into the cells in the INPUT section and set the desired level of confidence.  A significant (low) p-value suggests that we should reject the Null Hypothesis and that the difference between two means is statistically significant. This version of the test assumes that population variances for each subgroup are different.",null,null,null,null,null,null,null,null,null,null,null,"Sample 1","Sample 2",null,null,null,3]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Means",null,null,"x̅ᵣ"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Standard deviation",null,null,"sᵣ"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Size",null,null,"nᵣ",null,"critical value",{"$f":" IF( OK?, _xlfn.T.INV.2T( INDEX(level,level.index)/100, d.f. ), \"\" )","v":""}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":" IF(incomplete?,\"Please complete data entry\",IF(nonNumeric?,\"All input values must be numbers\",\"\"))","v":"Please complete data entry"}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":" IF( incomplete?, \"Please complete data entry\", \"\" )","v":"Please complete data entry"},null,null,null,null,"Variance"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND(NOT(incomplete?),stddev.invalid?),\"STANDARD DEVIATIONS MUST BE GREATER THAN ZERO!\", \"\" )","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND(size.invalid?,NOT(incomplete?)),\"SAMPLE NUMBERS MUST BE GREATER THAN ZERO!!\",\"\")","v":""}]
[null,null,null,null,"The test statistic is     "]
[]
[]
[]
[null,null,null,null,"where  "]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Result"]
[]
[null,null,null,null,"and"]
[null,null,null,null,"t     =","  t statistic"]
[null,null,null,null,"x̅₁   =","  Sample 1 Mean",null,null,null,null,null,null,null,null,null,"Difference: ",{"$f":"IF( OK?, (x̅₁ - x̅₂), IF(incomplete?,\"\",\"WHOOPS!\") )","v":""}]
[null,null,null,null,"x̅₂   =","  Sample 2 Mean",null,null,null,null,null,null,null,null,null,"Standard error: ",{"$f":" IF( OK?, SQRT( s₁²/ n₁ + s₂²/n₂ ), \"\" )","v":""}]
[null,null,null,null,"s₁    =","  Sample 1 Standard deviation",null,null,null,null,null,null,null,null,null,"Test statistic, t: ",{"$f":" IF( OK?, Δ / ᶓ, \"\" )","v":""}]
[null,null,null,null,"s₂    =","  Sample 2 Standard deviation",null,null,null,null,null,null,null,null,null,"d.f. : ",{"$f":" IF( OK?, ( s₁²/ n₁ + s₂²/n₂ )^2 / ( (s₁²/ n₁)^2 / (n₁-1) + (s₂²/n₂)^2 / (n₂-1) ), \"\" )","v":""}]
[null,null,null,null,"n₁   =","  Sample 1 size",null,null,null,null,null,null,null,null,null,"p-value: ",{"$f":" IF( OK?, _xlfn.T.DIST.2T( ABS(t), d.f.), \"\" )","v":""}]
[null,null,null,null,"n₂   =","  Sample 2 size"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Outcome: ",{"$f":" IF( OK?,\n           IF( ABS(t) > t‡,\n                \"SIGNIFICANT DIFFERENCE!\",\n                \"Difference not significant\")\n           & \" (at the \"& (level.selected) &\"% level)\",\n    \"\" )","v":""}]

{"sheet":"S2test3","index":12,"n_rows":36,"n_cols":22,"rows_kept":36,"cut":false,"hidden":false,"merged":[[11,4,17,10]]}
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"RefValues!Q24","v":"Same Samples (Repeated Measures)"}]
[]
[]
[]
[]
[]
[]
[null,null,null,null,"Notes",null,null,null,null,null,null,null,null,null,"Input",null,null,null,null,null,"Confidence level"]
[]
[null,null,null,null,"This test is used for testing,  WITHIN OBSERVATION,  differences on two statistics (e.g.  Likeability  scale for  Brand X  before  and  after  being  exposed  to  stimulus).   It tests the Null hypothesis that the mean of these differences in the population is zero. A significant (low) p-value suggests that we should reject the Null hypothesis and that that the mean of the differences is statistically significant.",null,null,null,null,null,null,null,null,null,null,null,"Mean of difference at individual level",null,"x̅D",null,null,1]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Std Dev. of difference at individual level",null,"sD"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sample size",null,"n"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"critical value",{"$f":" IF( OK?, _xlfn.T.INV.2T( INDEX(level,level.index)/100, d.f. ), \"\" )","v":""}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":" IF(incomplete?,\"Please complete data entry\",IF(nonNumeric?,\"All input values must be numbers\",\"\"))","v":"Please complete data entry"}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND(NOT(incomplete?),stdDev.invalid?),\"STANDARD DEVIATIONS MUST BE GREATER THAN ZERO!\", \"\" )","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND(size.invalid?,NOT(incomplete?)),\"RESPONDENT NUMBERS MUST BE GREATER THAN ONE!!\",\"\")","v":""}]
[]
[null,null,null,null,"The test statistic is     "]
[]
[]
[null,null,null,null,"where"]
[]
[null,null,null,null,"and",null,null,null,null,null,null,null,null,null,"Result"]
[null,null,null,null,"t     = ","  t statistic"]
[null,null,null,null,"x̅D   =","  Mean of difference at individual level"]
[null,null,null,null,"sD   = ","  Standard Deviation of difference at individual level"]
[null,null,null,null,"n    =","  Sample size",null,null,null,null,null,null,null,null,null,"Difference: ",{"$f":"IF( OK?, x̅ₔ, IF(incomplete?,\"\",\"WHOOPS!\") )","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Standard error: ",{"$f":" IF( OK?, sₔ / SQRT(n), \"\" )","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Test statistic, t: ",{"$f":" IF( OK?, Δ / ᶓ, \"\" )","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"d.f. : ",{"$f":" IF( OK?, n - 1, \"\" )","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"p-value: ",{"$f":" IF( OK?, _xlfn.T.DIST.2T( ABS(t), d.f.), \"\" )","v":""}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Outcome: ",{"$f":" IF( OK?,\n           IF( ABS(t) > t‡,\n                \"SIGNIFICANT DIFFERENCE!\",\n                \"Difference not significant\")\n           & \" (at the \"& (level.selected) &\"% level)\",\n    \"\" )","v":""}]

{"sheet":"Section3","index":13,"n_rows":18,"n_cols":16,"rows_kept":18,"cut":false,"hidden":false,"merged":[[11,4,28,10]]}
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"RefValues!Q25","v":"CONFIDENCE INTERVALS FOR PROPORTIONS"}]
[]
[]
[]
[]
[]
[]
[null,null,null,null,"Notes",null,null,null,null,null,null,null,null,null,"Contents Section 3"]
[]
[null,null,null,null,"This section offers a number of tests used for determining the confidence interval for estimates of proportion taken from a sample"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,1,{"$f":" S3.tests","v":"Proportion using Normal Confidence Interval"}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2,"Proportion using Wilson's Confidence Interval"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,3,"Total vs Subset"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,4,"Independent Samples"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,5,"Same Sample, Mutually Exclusive"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,6,"Same Sample, Overlapping"]

{"sheet":"S3test1","index":14,"n_rows":34,"n_cols":22,"rows_kept":34,"cut":false,"hidden":false,"merged":[[11,4,17,10]]}
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"RefValues!Q26","v":"Proportion using Normal Confidence Interval"}]
[]
[]
[]
[]
[]
[]
[null,null,null,null,"Notes",null,null,null,null,null,null,null,null,null,"Input",null,null,null,null,null,"Confidence level"]
[]
[null,null,null,null,"Provides a confidence interval for a sample estimate of proportion using the normal approximation to the binomial distribution.  Type the relevant values into the cells in the INPUT section and set the desired level of confidence. The range of possible values for the population proportion is shown. \n\nThis method should only be used when np or n(1-p) ≥5.",null,null,null,null,null,null,null,null,null,null,null,"Percentage sample:",null,"p̂%",null,null,2]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sample size",null,"n"]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"critical value",{"$f":" _xlfn.NORM.S.INV( 1 - INDEX(level,level.index)/100/2 )","v":1.9599639845400536}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":" IF(incomplete?,\"Please complete data entry\",IF(nonNumeric?,\"All input values must be numbers\",\"\"))","v":"Please complete data entry"}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(percent.invalid?,\"PERCENTAGES MUST BE BETWEEN 0 AND 100!\", \"\" )","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND(size.invalid?,NOT(incomplete?)),\"RESPONDENT NUMBERS MUST BE GREATER THAN ZERO!!\",\"\")","v":""}]
[]
[null,null,null,null,"The confidence interval is given by  "]
[]
[]
[]
[null,null,null,null,"where  "]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Result"]
[null,null,null,null,"C.I. ="," Confidence Interval"]
[null,null,null,null,"p̂   =","  Sample Proportion"]
[null,null,null,null,"n   =","  Sample size"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Percentage: ",{"$f":" IF( OK?, p̂⁰⁄₀,  IF(incomplete?,\"\",\"WHOOPS!\") )","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Standard error: ",{"$f":" IF( OK?, 100*SQRT( p̂*(1-p̂)/n ), \"\" )","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Critical value: ",{"$f":" IF( OK?, Z‡, \"\" )","v":""}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Confidence interval: ",{"$f":" IF( OK?, Δ  -  ᶓ * Z‡, \"\" )","v":""},{"$f":" IF( OK?, Δ +  ᶓ * Z‡, \"\" )","v":""}]

{"sheet":"S3test2","index":15,"n_rows":34,"n_cols":22,"rows_kept":34,"cut":false,"hidden":false,"merged":[[11,4,17,10]]}
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"RefValues!Q27","v":"Proportion using Wilson's Confidence Interval"}]
[]
[]
[]
[]
[]
[]
[null,null,null,null,"Notes",null,null,null,null,null,null,null,null,null,"Input",null,null,null,null,null,"Confidence level"]
[]
[null,null,null,null,"Provides a confidence interval for a sample estimate of proportion using the Wilson Score method.  Type the relevant values into the cells in the INPUT section and set the desired level of confidence. The range of possible values for the population proportion is shown. \n\nThis method can be used in all situations and is accurate when np and n(1-p) < 5 and for p close or equal to 0 or 100%",null,null,null,null,null,null,null,null,null,null,null,"Percentage sample:",null,"p̂%",null,null,2]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sample size",null,"n"]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"critical value",{"$f":" _xlfn.NORM.S.INV( 1 - INDEX(level,level.index)/100/2 )","v":1.9599639845400536}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":" IF(incomplete?,\"Please complete data entry\",IF(nonNumeric?,\"All input values must be numbers\",\"\"))","v":"Please complete data entry"}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(percent.invalid?,\"PERCENTAGES MUST BE BETWEEN 0 AND 100!\", \"\" )","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND(size.invalid?,NOT(incomplete?)),\"RESPONDENT NUMBERS MUST BE GREATER THAN ZERO!!\",\"\")","v":""}]
[]
[null,null,null,null,"The confidence interval is given by  "]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Result"]
[null,null,null,null,"where  "]
[]
[null,null,null,null,"C.I. ="," Confidence Interval"]
[null,null,null,null,"p̂   =","  Sample Proportion",null,null,null,null,null,null,null,null,null,null,"Percentage: ",{"$f":" IF( OK?, p̂⁰⁄₀,  IF(incomplete?,\"\",\"WHOOPS!\") )","v":""}]
[null,null,null,null,"n   =","  Sample size",null,null,null,null,null,null,null,null,null,null,"Standard error: ",{"$f":"IF(OK?,100*SQRT(p̂*(1-p̂)/n+(Z‡^2)/(n^2*4)),\"\")","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Critical value: ",{"$f":" IF( OK?, Z‡, \"\" )","v":""}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Confidence interval: ",{"$f":" IF( OK?,( p̂⁰⁄₀/100 +(Z‡^2)/(2*n)-  Z‡*ᶓ /100)/(1+(Z‡^2/n))*100, \"\" )","v":""},{"$f":" IF( OK?,( Δ/100  +(Z‡^2)/(2*n)+  Z‡*ᶓ /100)/(1+(Z‡^2/n))*100, \"\" )","v":""}]

{"sheet":"S3test3","index":16,"n_rows":34,"n_cols":22,"rows_kept":34,"cut":false,"hidden":false,"merged":[[11,4,17,10]]}
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"RefValues!Q17","v":"Total vs Subset"}]
[]
[]
[]
[]
[]
[]
[null,null,null,null,"Notes",null,null,null,null,null,null,null,null,null,"Input",null,null,null,null,null,"Level setting"]
[]
[null,null,null,null,"Provides a confidence interval for a sample estimate of the difference in a proportion between a subset (subgroup) and total.  Type the relevant values into the cells in the INPUT section and set the desired level of confidence. The range of possible values for the difference is shown. ",null,null,null,null,null,null,null,null,null,null,null,"Percentage for total:",null,"Ρ̂%",null,null,2]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Percentage for sub-group:",null,"p̂%"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Total respondents (base):",null,"Ν"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Number in sub-group (base):",null,"n",null,"critical value",{"$f":" _xlfn.NORM.S.INV( 1 - INDEX(level,level.index)/100/2 )","v":1.9599639845400536}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":" IF(incomplete?,\"Please complete data entry\",IF(nonNumeric?,\"All input values must be numbers\",\"\"))","v":"Please complete data entry"}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(percent.invalid?,\"PERCENTAGES MUST BE BETWEEN 0 AND 100!\", \"\" )","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND(NOT(incomplete?),size.invalid?),\"RESPONDENT NUMBERS MUST BE > 0 AND THE SUB-GROUP SHOULD BE SMALLER!!\",\"\")","v":""}]
[]
[null,null,null,null,"The confidence interval  is     "]
[]
[]
[]
[null,null,null,null,"where  "]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Result"]
[null,null,null,null,"C.I. ="," Confidence Interval"]
[null,null,null,null,"P̂  ="," Sample Proportion for Total"]
[null,null,null,null,"p̂  ="," Sample Proportion for Subset"]
[null,null,null,null,"N  ="," Total sample size",null,null,null,null,null,null,null,null,null,null,"Difference: ",{"$f":"IF( OK?, 100 * (p̂ - Ρ̂), IF(incomplete?,\"\",\"WHOOPS!\") )","v":""}]
[null,null,null,null,"n  ="," Subgroup sample size",null,null,null,null,null,null,null,null,null,null,"Standard error: ",{"$f":" IF( OK?, 100 * SQRT( Ρ̂*(1-Ρ̂)/n * (Ν-n)/Ν ), \"\" )","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Critical value: ",{"$f":" IF( OK?, Z‡, \"\" )","v":""}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Confidence interval: ",{"$f":" IF( OK?, Δ -  ᶓ * Z‡, \"\" )","v":""},{"$f":" IF( OK?,  Δ +  ᶓ * Z‡, \"\" )","v":""},null,{"$f":" IF( OK?, MIN(  Δ + ᶓ * Z‡,  0 ), 0 )","v":0}]

{"sheet":"S3test4","index":17,"n_rows":34,"n_cols":22,"rows_kept":34,"cut":false,"hidden":false,"merged":[[11,4,17,10]]}
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":" RefValues!Q29","v":"Independent Samples"}]
[]
[]
[]
[]
[]
[]
[null,null,null,null,"Notes",null,null,null,null,null,null,null,null,null,"Input",null,null,null,null,null,"Level setting"]
[]
[null,null,null,null,"Provides a confidence interval for a sample estimate of the difference in a proportion between two independent subgroups.  Type the relevant values into the cells in the INPUT section and set the desired level of confidence. The range of possible values for the difference is shown. ",null,null,null,null,null,null,null,null,null,null,null,"Sample proportion from subgroup 1:",null,"p̂₁%",null,null,2]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sample proportion from subgroup 2:",null,"p̂₂%"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sample size of subgroup 1:",null,"n₁"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sample size of subgroup 2:",null,"n₂",null,"critical value",{"$f":" _xlfn.NORM.S.INV( 1 - INDEX(level,level.index)/100/2 )","v":1.9599639845400536}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":" IF(incomplete?,\"Please complete data entry\",IF(nonNumeric?,\"All input values must be numbers\",\"\"))","v":"Please complete data entry"}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(percent.invalid?,\"PERCENTAGES MUST BE BETWEEN 0 AND 100!\", \"\" )","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":" IF(AND(size.invalid?,NOT(incomplete?)),\"RESPONDENT NUMBERS MUST BE GREATER THAN ZERO!!\",\"\")","v":""}]
[]
[null,null,null,null,"The confidence interval  is  "]
[]
[]
[]
[null,null,null,null,"where  "]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Result"]
[null,null,null,null,"C.I. ="," Confidence Interval"]
[null,null,null,null,"p̂₁  ="," Sample Proportion from subgroup 1"]
[null,null,null,null,"p̂₂  ="," Sample Proportion from subgroup 2"]
[null,null,null,null,"n₁  ="," Sample size of subgroup 1",null,null,null,null,null,null,null,null,null,null,"Difference: ",{"$f":"IF( OK?, 100 * (p̂₁ -  p̂₂), IF(incomplete?,\"\",\"WHOOPS!\") )","v":""}]
[null,null,null,null,"n₂  ="," Sample size of subgroup 2",null,null,null,null,null,null,null,null,null,null,"Standard error: ",{"$f":" IF( OK?,  100 * SQRT( p̂₁*(1-p̂₁)/n₁ + p̂₂*(1-p̂₂)/n₂ ), \"\" )","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Critical value: ",{"$f":" IF( OK?, Z‡, \"\" )","v":""}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Confidence interval: ",{"$f":" IF( OK?, Δ -  ᶓ * Z‡, \"\" )","v":""},{"$f":" IF( OK?,  Δ +  ᶓ * Z‡, \"\" )","v":""},null,{"$f":" IF( OK?, MIN(  Δ + ᶓ * Z‡,  0 ), 0 )","v":0}]

{"sheet":"S3test5","index":18,"n_rows":34,"n_cols":22,"rows_kept":34,"cut":false,"hidden":false,"merged":[[11,4,17,10]]}
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"RefValues!Q30","v":"Same Sample, Mutually Exclusive"}]
[]
[]
[]
[]
[]
[]
[null,null,null,null,"Notes",null,null,null,null,null,null,null,null,null,"Input",null,null,null,null,null,"Level setting"]
[]
[null,null,null,null,"Provides a confidence interval for an estimate of the difference between two mutually exclusive proportions from the same sample (e.g. Very Satisfied and Very Dissatisfied).  Type the relevant values into the cells in the INPUT section and set the desired level of confidence. The range of possible values for the difference is shown. ",null,null,null,null,null,null,null,null,null,null,null," Sample Proportion in A:",null,"p̂ₐ%",null,null,3]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null," Sample Proportion in B:",null,"p̂ᵦ%"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sample size:",null,"n"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"critical value",{"$f":" _xlfn.NORM.S.INV( 1 - INDEX(level,level.index)/100/2 )","v":1.6448536269514715}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":" IF(incomplete?,\"Please complete data entry\",IF(nonNumeric?,\"All input values must be numbers\",\"\"))","v":"Please complete data entry"}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(percent.invalid?,\"PERCENTAGES MUST BE BETWEEN 0 AND 100 AND TOTAL A MAXIMUM OF 100%!\", \"\" )","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND(size.invalid?,NOT(incomplete?)),\"RESPONDENT NUMBERS MUST BE GREATER THAN ONE!!\",\"\")","v":""}]
[]
[null,null,null,null,"The confidence interval  is     "]
[]
[]
[]
[null,null,null,null,"where  "]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Result"]
[null,null,null,null,"C.I. ="," Confidence Interval"]
[null,null,null,null,"p̂ₐ  ="," Sample Proportion in A"]
[null,null,null,null,"p̂ᵦ  ="," Sample Proportion in B"]
[null,null,null,null,"n    ="," Sample Size",null,null,null,null,null,null,null,null,null,null,"Difference: ",{"$f":"IF( OK?, 100 * (p̂ₐ - p̂ᵦ), IF(incomplete?,\"\",\"WHOOPS!\") )","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Standard error: ",{"$f":" IF( OK?, 100 *SQRT( (p̂ₐ*(1-p̂ₐ) +  p̂ᵦ*(1- p̂ᵦ) + 2*p̂ₐ*p̂ᵦ ) / (n - 1) ), \"\" )","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Critical value: ",{"$f":" IF( OK?, Z‡, \"\" )","v":""}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Confidence interval: ",{"$f":" IF( OK?, Δ -  ᶓ * Z‡, \"\" )","v":""},{"$f":" IF( OK?,  Δ +  ᶓ * Z‡, \"\" )","v":""},null,{"$f":" IF( OK?, MIN(  Δ + ᶓ * Z‡,  0 ), 0 )","v":0}]

{"sheet":"S3test6","index":19,"n_rows":34,"n_cols":22,"rows_kept":34,"cut":false,"hidden":false,"merged":[[11,4,17,10]]}
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[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"RefValues!Q31","v":"Same Sample, Overlapping"}]
[]
[]
[]
[]
[]
[]
[null,null,null,null,"Notes",null,null,null,null,null,null,null,null,null,"Input",null,null,null,null,null,"Level setting"]
[]
[null,null,null,null,"Provides a confidence interval for an estimate of the difference between two overlapping (multi-coded) proportions from the same sample (e.g. Awareness of Brand X and Brand Y).  Type the relevant values into the cells in the INPUT section and set the desired level of confidence. The range of possible values for the difference is shown. ",null,null,null,null,null,null,null,null,null,null,null,"Sample percentage in A:",null,"p̂ₐ%",null,null,2]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sample percentage in B:",null,"p̂ᵦ%"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null," Sample percentage in A AND B",null,"p̂ₐᵦ%"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sample size:",null,"n",null,"critical value",{"$f":" _xlfn.NORM.S.INV( 1 - INDEX(level,level.index)/100/2 )","v":1.9599639845400536}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":" IF(incomplete?,\"Please complete data entry\",IF(nonNumeric?,\"All input values must be numbers\",\"\"))","v":"Please complete data entry"}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(percent.invalid?,\n       \"PERCENTAGES MUST BE BETWEEN 0 AND 100!\",\n        IF( p̂ₐᵦ > MIN(p̂ₐ,p̂ᵦ),\n             \"p̂ₐᵦ cannot be greater than p̂ₐ or p̂ᵦ\",\n             \"\" )\n       )","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND(size.invalid?,NOT(incomplete?)),\"RESPONDENT NUMBERS MUST BE GREATER THAN ONE!!\",\"\")","v":""}]
[]
[null,null,null,null,"The confidence interval  is      "]
[]
[]
[]
[null,null,null,null,"where  "]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Result"]
[null,null,null,null,"C.I. ="," Confidence Interval"]
[null,null,null,null,"p̂ₐ  ="," Sample Proportion in A"]
[null,null,null,null,"p̂ᵦ  ="," Sample Proportion in B"]
[null,null,null,null,"p̂ₐᵦ ="," Sample Proportion in A AND B",null,null,null,null,null,null,null,null,null,null,"Difference: ",{"$f":"IF(incomplete?,\"\", IF(nonNumeric?,\"WHOOPS!\",IF( OK?, 100 * (p̂ₐ - p̂ᵦ),\"WHOOPS!\") ))","v":""}]
[null,null,null,null,"n    ="," Sample Size",null,null,null,null,null,null,null,null,null,null,"Standard error: ",{"$f":" IF(nonNumeric?,\"\", IF( OK?, 100 * SQRT( ( p̂ₐ* (1-p̂ₐ) +  p̂ᵦ* (1- p̂ᵦ) + 2 * ( p̂ₐ* p̂ᵦ - p̂ₐᵦ ) ) / (n - 1) ), \"\" ))","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Critical value: ",{"$f":" IF(nonNumeric?,\"\", IF( OK?, Z‡, \"\" ))","v":""}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Confidence interval: ",{"$f":"  IF(nonNumeric?,\"\",IF( OK?, Δ -  ᶓ * Z‡, \"\" ))","v":""},{"$f":" IF(nonNumeric?,\"\", IF( OK?,  Δ +  ᶓ * Z‡, \"\" ))","v":""},null,{"$f":"  IF(nonNumeric?,\"\",IF( OK?, MIN(  Δ + ᶓ * Z‡,  0 ), 0 ))","v":""}]

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[null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"RefValues!Q32","v":"CONFIDENCE INTERVALS FOR MEANS"}]
[]
[]
[]
[]
[]
[]
[null,null,null,null,"Notes",null,null,null,null,null,null,null,null,null,"Contents Section 4"]
[]
[null,null,null,null,"This section offers a number of tests used for determining the confidence interval for population means estimated from a sample"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,1,{"$f":" S4.tests","v":"Mean vs Hypothesised"}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,2,"Independent Samples (Unequal Variance)"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,3,"Same Samples (Repeated Measures)"]

{"sheet":"S4test1","index":21,"n_rows":34,"n_cols":22,"rows_kept":34,"cut":false,"hidden":false,"merged":[[11,4,17,10]]}
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[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"RefValues!Q33","v":"Mean vs Hypothesised"}]
[]
[]
[]
[]
[]
[]
[null,null,null,null,"Notes",null,null,null,null,null,null,null,null,null,"Input",null,null,null,null,null,"Confidence level"]
[]
[null,null,null,null,"Provides a confidence interval for a sample estimate of a mean statistic.  Type the relevant values into the cells in the INPUT section and set the desired level of confidence. The range of possible values for the mean is shown. ",null,null,null,null,null,null,null,null,null,null,null,"Sample mean",null,"x̅",null,null,1]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Hypothesised population mean",null,"μ₀"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sample standard deviation",null,"s"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sample size",null,"n",null,"critical value",{"$f":" IF( OK?, _xlfn.T.INV.2T( INDEX(level,level.index)/100, d.f. ), \"\" )","v":""}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":" IF(incomplete?,\"Please complete data entry\",IF(nonNumeric?,\"All input values must be numbers\",\"\"))","v":"Please complete data entry"}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND(NOT(incomplete?),stdDev.invalid?),\"STANDARD DEVIATIONS MUST BE GREATER THAN ZERO!\", \"\" )","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND(size.invalid?,NOT(incomplete?)),\"RESPONDENT NUMBERS MUST BE GREATER THAN ONE!!\",\"\")","v":""}]
[]
[null,null,null,null,"The confidence interval  is   "]
[]
[]
[]
[null,null,null,null,"where  "]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Result"]
[null,null,null,null,"C.I. ="," Confidence Interval"]
[null,null,null,null,"x̅    =","  Sample Mean"]
[null,null,null,null,"μ₀  =","  Hypothesised Population Mean"]
[null,null,null,null,"s     =","  Sample Standard Deviation",null,null,null,null,null,null,null,null,null,null,"Difference: ",{"$f":"IF( OK?, (x̅ - μ₀), IF(incomplete?,\"\",\"WHOOPS!\") )","v":""}]
[null,null,null,null,"n    =","  Sample size",null,null,null,null,null,null,null,null,null,null,"Standard error: ",{"$f":" IF( OK?, s / √n, \"\" )","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"d.f. : ",{"$f":" IF( OK?, n - 1, \"\" )","v":""},null,null,{"$f":" MAX( x̅, μ₀ )","v":0}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":" MIN( x̅, μ₀ )","v":0}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Confidence interval: ",{"$f":" IF( OK?, Δ -  ᶓ * t‡, \"\" )","v":""},{"$f":" IF( OK?,  Δ +  ᶓ * t‡, \"\" )","v":""},null,{"$f":" IF( OK?, MIN( Δ + ᶓ * t‡,  0 ) )","v":false}]

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[]
[]
[]
[]
[]
[]
[null,null,null,null,"Notes",null,null,null,null,null,null,null,null,null,"Input",null,null,null,null,null,"Confidence level"]
[]
[null,null,null,null,"Provides a confidence interval for a sample estimate of a difference in mean between two independent subgroups.  Type the relevant values into the cells in the INPUT section and set the desired level of confidence. The range of possible values for the difference in means is shown. ",null,null,null,null,null,null,null,null,null,null,null,"Sample 1","Sample 2",null,null,null,2]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Means",null,null,"x̅ᵣ"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Standard deviation",null,null,"sᵣ"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Size",null,null,"nᵣ",null,"critical value",{"$f":" IF( OK?, _xlfn.T.INV.2T( INDEX(level,level.index)/100, d.f. ), \"\" )","v":""}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":" IF(incomplete?,\"Please complete data entry\",IF(nonNumeric?,\"All input values must be numbers\",\"\"))","v":"Please complete data entry"}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND(NOT(incomplete?),stddev.invalid?),\"STANDARD DEVIATIONS MUST BE GREATER THAN ZERO!\", \"\" )","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND(size.invalid?,NOT(incomplete?)),\"SAMPLE NUMBERS MUST BE GREATER THAN ONE!!\",\"\")","v":""}]
[]
[null,null,null,null,"The confidence interval  is      "]
[]
[]
[]
[]
[null,null,null,null,"where",null,null,null,null,null,null,null,null,null,"Result"]
[]
[]
[null,null,null,null,"and"]
[null,null,null,null,"t     =","  t statistic",null,null,null,null,null,null,null,null,null,null,"Difference: ",{"$f":"IF( OK?, (x̅₁ - x̅₂), IF(incomplete?,\"\",\"WHOOPS!\") )","v":""}]
[null,null,null,null,"x̅₁    =","  Sample 1 Mean",null,null,null,null,null,null,null,null,null,null,"Standard error: ",{"$f":" IF( OK?, SQRT( s₁²/ n₁ + s₂²/n₂ ), \"\" )","v":""}]
[null,null,null,null,"x̅₂    =","  Sample 2 Mean",null,null,null,null,null,null,null,null,null,null,"d.f. : ",{"$f":" IF( OK?, ( s₁²/ n₁ + s₂²/n₂ )^2 / ( (s₁²/ n₁)^2 / (n₁-1) + (s₂²/n₂)^2 / (n₂-1) ), \"\" )","v":""},null,null,{"$f":" MAX( x̅₁, x̅₂ )","v":0}]
[null,null,null,null,"s₁     =","  Sample 1 Standard deviation",null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":" MIN( x̅₁, x̅₂ )","v":0}]
[null,null,null,null,"s₂     =","  Sample 2 Standard deviation",null,null,null,null,null,null,null,null,null,null,"Confidence interval: ",{"$f":" IF( OK?, Δ -  ᶓ * t‡, \"\" )","v":""},{"$f":" IF( OK?,  Δ +  ᶓ * t‡, \"\" )","v":""},null,{"$f":" IF( OK?, MIN( Δ + ᶓ * t‡,  0 ), \"\" )","v":""}]
[null,null,null,null,"n₁    =","  Sample 1 size"]
[null,null,null,null,"n₂    =","  Sample 2 size"]

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[]
[]
[]
[]
[]
[null,null,null,null,"Notes",null,null,null,null,null,null,null,null,null,"Input",null,null,null,null,null,"Confidence level"]
[]
[null,null,null,null,"Provides a confidence interval for a sample estimate of mean WITHIN OBSERVATION differences between two statistics (e.g. Likeability scale for Brand X before and after being exposed to stimulus).  Type the relevant values into the cells in the INPUT section and set the desired level of confidence. The range of possible values for the mean of the differences is shown. ",null,null,null,null,null,null,null,null,null,null,null,"Sample mean",null,"x̅ₔ",null,null,3]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sample standard deviation",null,"sₔ"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sample size",null,"n"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"critical value",{"$f":" IF( OK?, _xlfn.T.INV.2T( INDEX(level,level.index)/100, d.f. ), \"\" )","v":""}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":" IF(incomplete?,\"Please complete data entry\",IF(nonNumeric?,\"All input values must be numbers\",\"\"))","v":"Please complete data entry"}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND(NOT(incomplete?),stdDev.invalid?),\"STANDARD DEVIATIONS MUST BE GREATER THAN ZERO!\", \"\" )","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND(size.invalid?,NOT(incomplete?)),\"RESPONDENT NUMBERS MUST BE GREATER THAN ONE!!\",\"\")","v":""}]
[]
[null,null,null,null,"The confidence interval  is   "]
[]
[]
[null,null,null,null,"where  "]
[]
[null,null,null,null,"and",null,null,null,null,null,null,null,null,null,"Result"]
[null,null,null,null,"t     =","  t statistic"]
[null,null,null,null,"x̅D  =","  Sample Mean"]
[null,null,null,null,"sD   = ","  Sample Standard Deviation"]
[null,null,null,null,"n     =","  Sample size",null,null,null,null,null,null,null,null,null,null,"Difference: ",{"$f":"IF( OK?, x̅ₔ, IF(incomplete?,\"\",\"WHOOPS!\") )","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Standard error: ",{"$f":" IF( OK?, sₔ / SQRT(n), \"\" )","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"d.f. : ",{"$f":" IF( OK?, n - 1, \"\" )","v":""}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Confidence interval: ",{"$f":" IF( OK?, Δ -  ᶓ * t‡, \"\" )","v":""},{"$f":" IF( OK?,  Δ +  ᶓ * t‡, \"\" )","v":""},null,{"$f":" IF( OK?, MIN( Δ + ᶓ * t‡,  0 ), 0 )","v":0}]

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[null,null,null,null,null,null,null,null,null,null,"CONTENTS"]
[null,null,null,null,null,null,null,null,null,null,"HYPOTHESIS PROPORTIONS"]
[1,null,null,null,null,null,null,null,null,null,"Sample vs hypothesised"]
[2,null,null,null,null,null,null,null,null,null,"Total vs subset"]
[3,null,null,null,null,null,null,null,null,null,"Independent samples",null,null,"(a) Equal variance",null,"(b) Different variance"]
[5,null,null,null,null,null,null,null,null,null,"Same sample exclusive"]
[6,null,null,null,null,null,null,null,null,null,"Same sample overlapping"]
[null,null,null,null,null,null,null,null,null,null,"HYPOTHESIS MEANS"]
[7,null,null,null,null,null,null,null,null,null,"Mean vs hypothesis"]
[8,null,null,null,null,null,null,null,null,null,"Independent samples",null,null,"(a) Equal variance",null,"(b) Different variance"]
[10,null,null,null,null,null,null,null,null,null,"Repeated measures"]
[null,null,null,null,null,null,null,null,null,null,"CONFIDENCE PROPORTIONS"]
[11,null,null,null,null,null,null,null,null,null,"Proportion - Normal CI"]
[null,null,null,null,null,null,null,null,null,null,"Proportion - Wilson's CI"]
[12,null,null,null,null,null,null,null,null,null,"Total vs subset"]
[13,null,null,null,null,null,null,null,null,null,"Independent samples"]
[14,null,null,null,null,null,null,null,null,null,"Mutually exclusive"]
[15,null,null,null,null,null,null,null,null,null,"Overlapping"]
[null,null,null,null,null,null,null,null,null,null,"CONFIDENCE MEANS"]
[16,null,null,null,null,null,null,null,null,null,"Mean vs hypothesis"]
[17,null,null,null,null,null,null,null,null,null,"Independent samples",null,null,"Unequal variance"]
[18,null,null,null,null,null,null,null,null,null,"Same samples, rept. measures"]

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[null,"Level","statistic","confidence",null,"thresholds"]
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[null,10,1.6448536269514726,90,null,2.3263478740408408]
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[]
[]
[]
[]
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[null,null,null,null,null,null,null,"STATISTICAL TESTS"]
[null,null,null,null,null,null,null,"0         CONTENTS"]
[null,null,null,null,null,null,null,"1         HYPOTHESIS TESTS FOR PROPORTIONS",null,null,null,null,null,null,null,null,{"$f":" MID( H15, 11, 100 )","v":"HYPOTHESIS TESTS FOR PROPORTIONS"}]
[null,null,null,null,null,null,null,"1.1       Proportion vs Hypothesised",null,null,null,null,null,null,null,null,{"$f":" \"Sample\" & MID( H16, FIND( \"n\", H16 )+1, 100 )","v":"Sample vs Hypothesised"}]
[null,null,null,null,null,null,null,"1.2       Proportion: Total vs Subset",null,null,null,null,null,null,null,null,{"$f":" MID( H17, FIND( \":\", H17 )+2, 100 )","v":"Total vs Subset"}]
[null,null,null,null,null,null,null,"1.3       Two Proportion: Independent Samples",null,null,null,null,null,null,null,null,{"$f":" MID( H18, FIND( \":\", H18 )+2, 100 )","v":"Independent Samples"},null,null,"(a) ","Equal Variance",null,"(b) ","Different Variance"]
[null,null,null,null,null,null,null,"1.4       Two Proportions: Same Sample, Mutually Exclusive",null,null,null,null,null,null,null,null,{"$f":" MID( H19, FIND( \":\", H19 )+2, 100 )","v":"Same Sample, Mutually Exclusive"}]
[null,null,null,null,null,null,null,"1.5       Two Proportions: Same Sample, Overlapping",null,null,null,null,null,null,null,null,{"$f":" MID( H20, FIND( \":\", H20 )+2, 100 )","v":"Same Sample, Overlapping"}]
[null,null,null,null,null,null,null,"2         HYPOTHESIS  TESTS FOR MEANS",null,null,null,null,null,null,null,null,{"$f":" MID( H21, 11, 100 )","v":"HYPOTHESIS  TESTS FOR MEANS"}]
[null,null,null,null,null,null,null,"2.1       Mean vs Hypothesised",null,null,null,null,null,null,null,null,{"$f":" \"Mean\" & MID( H22, FIND( \"n\", H22 )+1, 100 )","v":"Mean vs Hypothesised"}]
[null,null,null,null,null,null,null,"2.2       Two Means: Independent Samples",null,null,null,null,null,null,null,null,{"$f":" MID( H23, FIND( \":\", H23 )+2, 100 )","v":"Independent Samples"},null,null,"(a) ","Equal Variance",null,"(b) ","Different Variance"]
[null,null,null,null,null,null,null,"2.3       Two Means: Same Samples (Repeated Measures)",null,null,null,null,null,null,null,null,{"$f":" MID( H24, FIND( \":\", H24 )+2, 100 )","v":"Same Samples (Repeated Measures)"}]
[null,null,null,null,null,null,null,"3         CONFIDENCE INTERVALS FOR PROPORTIONS",null,null,null,null,null,null,null,null,{"$f":" MID( H25, 11, 100 )","v":"CONFIDENCE INTERVALS FOR PROPORTIONS"}]
[null,null,null,null,null,null,null,"3.1      Proportion using Normal Confidence Interval",null,null,null,null,null,null,null,null,{"$f":" MID( H26, 10, 100 )","v":"Proportion using Normal Confidence Interval"}]
[null,null,null,null,null,null,null,"3.2      Proportion using Wilson's Confidence Interval",null,null,null,null,null,null,null,null,{"$f":" MID( H27, 10, 100 )","v":"Proportion using Wilson's Confidence Interval"}]
[null,null,null,null,null,null,null,"3.3       Proportion: Total vs Subset",null,null,null,null,null,null,null,null,{"$f":" MID( H28, FIND( \":\", H28 )+2, 100 )","v":"Total vs Subset"}]
[null,null,null,null,null,null,null,"3.4       Two Proportion: Independent Samples",null,null,null,null,null,null,null,null,{"$f":" MID( H29, FIND( \":\", H29 )+2, 100 )","v":"Independent Samples"}]
[null,null,null,null,null,null,null,"3.5       Two Proportions: Same Sample, Mutually Exclusive",null,null,null,null,null,null,null,null,{"$f":" MID( H30, FIND( \":\", H30 )+2, 100 )","v":"Same Sample, Mutually Exclusive"}]
[null,null,null,null,null,null,null,"3.6       Two Proportions: Same Sample, Overlapping",null,null,null,null,null,null,null,null,{"$f":" MID( H31, FIND( \":\", H31 )+2, 100 )","v":"Same Sample, Overlapping"}]
[null,null,null,null,null,null,null,"4         CONFIDENCE INTERVALS FOR MEANS",null,null,null,null,null,null,null,null,{"$f":" MID( H32, 11, 100 )","v":"CONFIDENCE INTERVALS FOR MEANS"}]
[null,null,null,null,null,null,null,"4.1       Mean vs Hypothesised",null,null,null,null,null,null,null,null,{"$f":" \"Mean\" & MID( H33, FIND( \"n\", H33 )+1, 100 )","v":"Mean vs Hypothesised"}]
[null,null,null,null,null,null,null,"4.2       Two Means: Independent Samples (Unequal Variance)",null,null,null,null,null,null,null,null,{"$f":" MID( H34, FIND( \":\", H34 )+2, 100 )","v":"Independent Samples (Unequal Variance)"}]
[null,null,null,null,null,null,null,"4.3       Two Means: Same Samples (Repeated Measures)",null,null,null,null,null,null,null,null,{"$f":" MID( H35, FIND( \":\", H35 )+2, 100 )","v":"Same Samples (Repeated Measures)"}]