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### Example 1: Independent samples

<img src="/uploads/upload/image/5200/direct/1658780910718-1658780910718.png" alt="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'"." class="fr-fic fr-dib">

### Example 2: Paired samples

### Example 3: Paired samples

<img src="/uploads/upload/image/5200/direct/1658780957805-1658780957805.png" alt="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."" class="fr-fic fr-dib">

### Download

[Protobi Stats tests - Independent and paired samples 2022-07-05.pptx](/uploads/upload/image/5200/direct/1663004934387-Protobi%20Stats%20tests%20-%20Independent%20and%20paired%20samples%202022-07-05.pptx)

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