PSYC2001 Mid-Term (Theory)

Effect size

Difference between the observed data and the value specified in the null hypothesis.

Why the decision rule for a t-test is to reject H0 if |t| >_ tc

• t captures the effect size in units of standard error.

• tc: the value of t that cuts off alpha/2 of the area under the t distribution in each of the 2 tails (assuming H0 is true).

• If t > tc: the probability of the observed t occurring by chance under H0 is less than alpha error rate → reject H0.

• If t < tc: the probability of the observed t under H0 is more than alpha error rate → retain H0.

Why an interval estimate is better than a point estimate

• Point estimate: single best estimate e.g. M.

• Interval estimate: point estimate + range of values.

• Can specify the degree of confidence (level of alpha) used to find parameter.

• E.g. a = 0.05 → 5% chance of making an error (population mean is outside the interval) but 95% chance of being correct.

Assess effect size of paired samples

In a repeated measures design, the appropriate analysis to assess effect size is a confidence interval.

If we reject a null hypothesis, is it false?

• No.

• 5% probability that H0 is actually true.

• That is why alpha 0.05 significance level is a Type 1 error rate (false positives).

• 5% significance level → we will mistakenly reject true null hypotheses 5% of the time.