HYPOTHESIS TESTING ; Paired Sample T-Test

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Last updated 9:40 PM on 4/24/26
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5 Terms

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Why do we use Paired Sample t-tests?

Test difference in mean scores for a sample comprising matched pairs

  • pre + post intervention on same individual

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How do you get the t-statistic

d¯ = mean of individual difference scores (di)

  • di = xi1 − xi2

μd0 = hypothesised population mean difference in the null

  • assumed to be 0

SEd = SE of mean difference (d)

  • sd = SD of the difference scores (di)

  • n = sample size / number of matched pairs

essentially a one sample t-test on the difference scores

<p>d¯ = mean of individual difference scores (di) </p><ul><li><p>di = xi1 − xi2</p></li></ul><p>μd0 = hypothesised population mean difference in the null </p><ul><li><p>assumed to be 0 </p></li></ul><p>SEd = SE of mean difference (d)</p><ul><li><p>sd = SD of the difference scores (di)</p></li><li><p>n = sample size / number of matched pairs </p></li></ul><p></p><p>essentially a one sample t-test on the difference scores </p><p></p>
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Hypothesis notation

Two-Tailed

  • Null = population mean of difference scores = hypothesised population mean difference scores

One-Tailed

  • less or greater than

<p>Two-Tailed</p><ul><li><p>Null = population mean of difference scores = hypothesised population mean difference scores </p></li></ul><p>One-Tailed</p><ul><li><p>less or greater than</p></li></ul><p></p>
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Data Requirements

Numeric Value

Normality

Homogeneity across pairs

Assumptions concern difference scores

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Cohen’s D

d¯ = mean of difference scores

μd0 = hypothesised difference in means in the null

sd = SD of difference scores

<p>d¯ = mean of difference scores</p><p>μd0 = hypothesised difference in means in the null</p><p>sd = SD of difference scores </p>