lecture 7 + 10 (stats) Flashcards
What is an independent t-test used for?
to compare two means from different groups (i.e., independent conditions)
When is a paired-samples t-test used?
A paired-samples t-test, or dependent t-test, is used to compare two means from the same or related entities (i.e., repeated measures or matched samples)
What is the rationale behind the t-test?
if two samples come from the same population, their means should be roughly equal under the null hypothesis, and any difference reflects sampling variation
steps to get a t distribution?
- take a random sample from a population
- calculate the mean and the standard deviation of the sample
- determine the SE of the sample
- calculate t statistic
- repeat the process with multiple random samples of the same size
- Each sample’s t-value will make up the t distribution (which is a sampling distribution)
what is the t statistic?
represents the deviation of the sample mean from the population mean, considering the sample size, expressed as the degree of freedom = n – 1
large sample size and its consequences?
- the higher the sample size the lower the SE
- when sample size large enough, t distribution is normally distributed
What is the role of the standard error in a t-test?
measures how much sample means fluctuate, allowing comparison of the observed mean difference to the expected difference under the null hypothesis
main difference paired samples and indepedent t test equation?
- how we arrive at the values of interest
- with independent samples we’re not dealing with difference scores because there’s no connection between scores in the two conditions that we want to compare
independent t test equation and sample sizes?
equation is only true when the sample sizes are equal
How do you run an independent t-test in JASP?
- Click on t-test in the analysis menu
- Select “Classical Independent Samples t-test.”
- Transfer the outcome variable to the variable box and the predictor variable to the grouping box.
- Set confidence intervals (CI) and effect size options
How do you run a paired-samples t-test in JASP?
- Select “Classical Paired Samples t-test.”
- Transfer pairs of variables to the variables pairs box.
- Ensure effect size and Cohen’s d are selected.
- If using repeated measures, select “Correct for Correlations.”
What additional statistics should you report in a t-test?
Report confidence intervals (CI) for parameters and effect size, such as Cohen’s d
effect size d (Cohen’s d)?
- the standardized difference between the mean and the expected μ
- in the t-test, effect-size can be expressed as d (Cohen’s d)
- independent of sample size
- 0 to 0.1 small effect sizes, 0.1 to 0.3 medium effect sizes, 0.3 to 0.5 large effect sizes
effect size r?
- another way to express effect size
- similar to correlation coefficient
Why do paired-samples t-tests have more statistical power than independent samples t-tests?
because they reduce unsystematic variance by using the same participants across conditions, making it easier to detect systematic variance
How should comparisons between two means be reported?
State the finding alongside the test statistics, degrees of freedom, probability value, effect size, and include a visual aid like a raincloud plot
assumptions independent t test?
- independence of observations
- normality
- equal variances
check homogeneity on jasp?
with levene test
check normality assumption on jasp?
- using hypothesis test (Shapiro-Wilk): p < a -> assumption violated
- Assess using a plot (Q-Q plot): Points should be along the diagonal
how to handle violations on jasp?
- Unequal variance: Welch t-test
- Non-normality: nonparametric test
assumptions of paired samples t testing?
- differences between paired observations should be indepedent
- normality of differences
assumptions NHST?
- random sampling
- normality
- measurement level (interval or ratio)
t vale for two sided NHST test?
Need a higher t-value when doing a two-sided test since the alpha is spread across two tales
