Week 4: Statistical Hypothesis Testing and t-Tests

What is the main goal of statistical hypothesis testing in the context of t-tests?

To determine if a difference between group means is 'real' or due to chance.

What does the null hypothesis (H0) state in statistical hypothesis testing?

It states that there is no difference between group means.

When do we reject the null hypothesis (H0)?

We reject H0 if the result is 'very unlikely' under the null hypothesis.

What distribution is used for t-tests instead of the z-distribution?

The t-distribution is used because the population standard deviation is unknown.

How does the shape of the t-distribution change?

It changes based on sample size/degrees of freedom (df), being broader with thicker tails for lower df and more like a normal distribution for larger df.

What is the formula for calculating the t-statistic?

The t-statistic is calculated using the sample mean (M), population mean under H0 (mu), and the estimated standard error of the mean (sM).

What is variance (s^2) in the context of t-tests?

Variance is a measure of deviation in the sample, calculated by dividing the sum of squared differences (SS) by the degrees of freedom (df).

What is the formula for degrees of freedom (df) in a one-sample t-test?

For a one-sample t-test, df = n - 1.

What is the significance of the alpha level in hypothesis testing?

The alpha level determines how unlikely a result must be to reject H0, with a conventional value of .05 in psychology.

What are the two types of hypotheses in hypothesis testing?

Directional hypotheses (expecting a difference in a specific direction) and non-directional hypotheses (expecting any difference).

What is the difference between a one-tailed test and a two-tailed test?

A one-tailed test assesses a specific direction of difference, while a two-tailed test assesses any difference.

What are effect size measures used for in t-tests?

Effect size measures quantify the magnitude of an effect independently of sample size.

What is Cohen's d?

Cohen's d is an estimate of the mean difference divided by the standard deviation, with conventional cut-off values of 0.2 (small), 0.5 (medium), and 0.8 (large).

What does r-squared (r^2) represent in the context of t-tests?

R-squared estimates the percentage of variation explained by the experimental manipulation.

What are Confidence Intervals (CIs)?

CIs are ranges of values centered around a sample statistic, providing an estimate of where the corresponding population parameter likely lies.

What assumptions must be met for running t-tests?

Independent observations, normal populations, and equal variances for independent-measures.

What is the logic of hypothesis testing?

Assume the H0 is true and reject it only if the observed data is very unlikely under that assumption.

What is the reporting format for statistical results in psychology?

Italicize statistics letters (t, r^2), report df in brackets, report exact p-values, omit leading zero for numbers less than 1, and report one effect size measure.

What is the empirical t-value compared against?

It is compared to a critical t-value from a t-distribution table using the appropriate degrees of freedom.

What is the pooled variance in the context of independent-measures t-tests?

Pooled variance is the average of the two sample variances, calculated by summing the SS from each group and dividing by the sum of the dfs.

What is the focus of the paired-samples t-test?

The focus is on the difference scores between two conditions for each participant.

How is the standard error of the mean difference calculated in paired-samples t-tests?

It is calculated from the variance of the difference scores.

What does a statistically significant result in a t-test indicate?

It indicates that the difference is unlikely due to chance, but does not indicate the magnitude or meaningfulness of the effect.

What is the importance of understanding how t-statistics are calculated?

It is important for understanding statistics and evaluating scientific publications.