Comparing percentages:Independent vs paired samples

Updated at 2022-07-25 20:25:05 UTC

Side-by-side comparison showing "Independent samples" (two separate groups of black and white circles) using Z test formula with p1-p2, versus "Paired samples" (circles connected by arrows) using McNemar's test with chi-squared formula. Text explains when to use each method for comparing different or same respondents.

Example 1: Independent samples

Two groups of circles (black=Yes, white=No) with left showing "40 respondents, 10 'Yes' answers, 25% positive" and right labeled "Sample B" showing "40 respondents, 17 'Yes' answers, 42.5% positive". Below displays Z-test calculation: z = (0.425 - 0.25) / sqrt((27/80)(53/80)[1/40 + 1/40]) = 1.65, with p = 0.098 > 0.05, concluding "Difference is 'Not significant'".

Example 2: Paired samples

Left side shows "40 respondents, 10 'Yes' answers, 25% positive" with paired connections to right side "40 respondents, 17 'Yes' answers, 42.5% positive". Blue brackets highlight "1 switch 'Yes' to 'No'" (white to black circles) and "8 switch 'No' to 'Yes'" (white to black circles). McNemar's calculation: z = ((|8-1|-1)^2)/(8+1) = 4.0, p = 0.046 < 0.05, concluding "Difference is 'Significant'". Text explains "Out of 9 switches, 8 are from 'No' to 'Yes'. Switches are significantly more likely to be from 'No' to 'Yes' than the other way."

Example 3: Paired samples

Paired comparison labeled "Question A:" (40 respondents, 10 'Yes', 25% positive) and "Question B:" (40 respondents, 17 'Yes', 42.5% positive) with arrows connecting responses. Blue brackets show "3 switch 'Yes' to 'No'" and "10 switch 'No' to 'Yes'". McNemar's calculation: z = ((|10-3|-1)^2)/(10+3) = 2.77, p = 0.098 > 0.05, concluding "Difference is 'Not significant'". Text explains "Out of 13 switches, 10 are from 'No' to 'Yes' versus 3 from 'Yes' to 'No'. Here switches are not significantly more likely to be from 'No' to 'Yes' than the other way."

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Protobi Stats tests - Independent and paired samples 2022-07-05.pptx