T-tests

• Goal of experiments


  To determine if the independent variable has a systematic effect on the dependent variable
• Sampling error


  The difference between the population and the sample that represents the population
• Differences among groups (or conditions): Does the mean for one group differ from the mean of the other group?
• Null hypothesis


  Group 1 Mean = Group 2 Mean (M1 = M2), The IV did not have an effect on the DV
• Alternative Hypothesis


  M1 ≠ M2, M1 > M2, M1 < M2, The IV did have an effect on the DV
• To determine differences between means, use the difference between the group means
• To determine the variability around the group means, use the amount of variability within each condition
• Ratio of variability between groups to variability within groups


  The more extreme the ratio, the more likely it is that group differences were the result of your manipulation and not sampling error
• Calculating a t-value and p-value


  1. t = (M1 - M2) / SE_difference

  2. Use the t-value to calculate a p-value

  3. Compare the p-value to the alpha level
• Null Hypothesis Test


  • If p > .05, fail to reject the null-hypothesis, no good evidence that our groups differ, we cannot say that our IV had an effect
  • If p < .05, reject the null-hypothesis in favor of the alternative, there is good evidence that our groups are not equal, we can say that our IV had an effect
• For t to be equal to zero, the mean difference needs to be equal to the mean difference we would expect due to sampling error
• If the mean difference is equal to the mean difference we would expect due to sampling error, there is no effect, our differences can be explained by sampling error
• Sufficient information to allow readers to understand the test conducted: test statistic, degrees of freedom, p-value, one-tailed or two-tailed test, Ms, SDs, Ns, effect sizes with confidence intervals
• Writing results in APA format


  • Without effect size: Words words words, t(127) = 3.51, p = .031, one-tailed
  • With effect size: Words words words, t(127) = 4.52, p < .001, two-tailed, d = 0.75, 95% CI [0.50, 1.00]
• Stats-then-explanation


  1. First sentence: Stats

  2. Second sentence: Explanation