T-tests

• what does a t-test do?

  a t-test is used when our IV is a category. specifically a category with two levels. the DV is continuous.

  tests whether there is a significant difference between the mean of two groups

  can use correlation but that doesn't = causality

  categorical IV allows for an experimental test
• Mean graphs 1

  Small mean difference - large variance

  Unlikely to be a significant difference

  
• mean graphs 2

  Large mean difference - large variance

  More likely to be a significant difference

  
• mean graphs 3

  Small mean difference - small variance

  More likely to be a significant difference

  
• Mean graphs 4

  Tiny mean difference- small variance

  Unlikely to be a significant difference

  
• t-tests

  one of the most widely used stats tests

  generally, two types of t-tests. those used for within-subjects design and those used for between-subjects design.
• within subjects design

  Name = paired samples, dependent samples, related samples

  
  

  compares means from the same group (all participants) but at different times (before vs after treatment, time 1 vs time 2 etc.)
• Between subjects design

  Name = unpaired samples, independent samples, unrelated samples, alt: Welch’s test

  
  

  Compares the means of two independent groups
• students (independent) test

  WILLIAM GOSSET created t-test, published under name ‘student’
• independent t-test

  Design - between subjects design, comparing two different groups

  Assumptions - data must be continuous/scale (i.e. interval or ratio), data should be approximately normally distributed, data must have homogeneity of variance (i.e. variance between groups are equal)

  
  

  These can be naturally occurring groups (e.g. sex) or experimental groups (e.g. drugs vs placebo)
• naturally occurring groups

  these are known as quasi experimental designs

  they have a fundamental problem - you cant infer causality from them
• experimental groups

  we can infer causality from them if:

  • randomise ppts to groups - balances characteristics across groups

  Randomised control trials are the gold standard of evidence

  Can match groups, but is harder to do and time consuming
• Independent samples t-test: theory

  R studios does this automatically

  
• Homoscedasticity/Homogeneity of variance

  Here the SD’s are similar

  This shows homogeneity of variance

  
• heteroscedasticity/heterogeneity of variance


  The variance is not similar, they are vastly different

  This shows heterogeneity of variance

  
• how to know if we have HoV

  Levene’s test: tests the null hypothesis that the population variances are equal

  if Levene’s test is significant (p < .05) then HoV is violated

  -> leads to increased likelihood that significant effect will be found when there isn’t one (false positive; type 1 error)

  DO NOT report Levene’s test in a report. report either: equal variances assumed or equal variances not assumed
• code for independent samples t-test

  leveneTest(DV~IV, data=X)

  t.test(DV~IV)

  Test with homogeneity assumed -> t.test(DV~IV, var.equal = TRUE)
• writing up independent t-test

  an independent-samples t-test didn’t/violated the assumption of HoV snd so equal variances were/not assumed. results showed that (…) in the (…) condition were statistically significantly (…) than in the (…) condition, 𝘵(df) = XX.XX, 𝘱 = .XXX, 𝘥 = X.XX [95% CI: X.XX, X.XX]
• effect size

  p-value doesnt tell us if our effect is big, small or important. if sample is big enough, there will always be a significant difference

  effect size is how big the difference between the two groups means are

  can be small, medium or large
• Cohen’s d

  0.2 = small effect size

  0.5 = medium effect size

  0.8 = large effect size

  cohen.d(DV~IV)
• confidence intervals

  an interval which is expected to typically contain the parameter being estimated

  95% CIs given as a rule, 95% confident the parameter falls between the intervals

  narrow CIs = precise estimate

  wide CIs = imprecise estimate
• Welch’s test

  an alternative to the independent t-test which does not assume HoV
• Paired-samples t-test

  Design - within-subjects design. Comparing one group at two different time points or conditions

  Assumptions - data must be continuous/scale (i.e. interval or ratio), data must be normally distributed

  Can be naturally occurring or experimental groups
• Paired-samples t-test code

  t.test(…, …, paired = TRUE)

  Comma not tilda as there isn’t an IV and DV per se

  cohen.d(…, …, paired = TRUE)
• Paired-samples t-test write up

  a paired-samples t-test showed that reaction times in the … condition were statistically significantly … than in the … condition (mean difference = X.XX), t(df)= XX.XX, p = .XXX, d = X.XX [95% CI: X.XX, X.XX]

  can also highlight the effect size
• graphing results from t-test

  bar charts most common method, but boxplots are better