T-test

• Independent samples t-tests - Used when you want to compare the mean scores of two different groups of people or conditions.
• Paired samples t-test - Used when you want to compare the means scores for the same group of people on two different occasions or when you have matched pairs.
• INDEPENDENT SAMPLES T-TESTS

  • Independent-measures t-test

  • Between-subjects t-test

  • Unpaired t-test

  • Student’s t-test
• PAIRED SAMPLES T-TEST

  • Dependent samples t-test

  • Paired-difference t-test

  • Matched pairs t-test

  • Repeated-samples t-test
• The t statistic is used to test hypotheses about an unknown population mean, μ, when the value of  is unknown. The formula for the t statistic has the same structure as the z-score formula, except that the t statistic uses the estimated standard error in the denominator.
• A t distribution is the complete set of t values computed for every possible random sample for a specific sample size (n) or a specific degrees of freedom (df).
• Cohen's d is a measure of the correlation between two sets of data.

  The mean difference over standard deviation (mean of the treatment group minus the mean of the no treatment group over standard deviation

  • 0.2= small
  • 0.5 = medium
  • 0.8 = large
• If all other factors are held constant, a confidence interval computed from a sample of n = 25 is wider than a confidence interval computed from a sample of n = 100.
• If all other factors are held constant, an 80% confidence interval is not wider than a 90% confidence interval.
• To compute the t statistic, you must first calculate the sample variance (or standard deviation) as a substitute for the unknown population value.
• Assumptions of paired t-test:

  • level of measurement: interval or ratio level (continuous).
  • normally distributed
  • the difference between the two scores should be normally distributed. With sample sizes of 30+.
• Eta squared is an effect size that is used to compare the magnitude of the difference between two groups. $Eta squared =$$t^2 / t^2 +$$(N - 1)$
• T-test for two independent samples - test for difference in means between two independent samples
• Independent Samples T-test - used to compare the means of two independent samples. You are testing the probability that the two sets of scores came from the same population.
• T-test informs us whether the difference between group means are “real”, but it does not inform us the “size” of the difference.