# PSYCH 100A Lecture Notes - Lecture 6: Sampling Distribution, F-Distribution, Null Hypothesis

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Published on 28 Mar 2018

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Lecture 6

Within-group research design: seeks to compare two or more measurements of variables from

the same participants

• Does’t euie itevetios

• Scores don't need to be from the same person

• A classic within-group design collects two or more repeated measurements from the same

group of individuals (pretest and posttest)

Paired-samples t-test

• Appropriate for within-group designs with two measurements

• Outcome variable must be continuous

Difference (change) scores:

• The paired-samples t test requires two scores per individual (pretest and posttest)

• Hypotheses and computations involve difference scores that subtract the two variables

• Diff = x2 - x1 = posttest - pretest

o If increase from pre --> post then positive

o If decrease from pre --> post then negative

Null hypothesis

• Vast majority of pretest-posttest designs specify a null hypothesis of no change

• States that the mean different or change in the full population is zero

• H: μ_diff =

Alternate hypothesis

• What kind of effect can we expect to see?

• Requires a two-tailed p-value

S_xdiff = s_diff

One- factor ANOVA: appropriate for research scenarios with a categorical independent variable

and one numeric (continuous) dependent variable

• One-factor = one independent variable

• Independent-samples t test was used to compare means of two groups

• ANOVA is appropriate for between-group designs with two or more groups

ANOVA tests whether the package of group differences have anything significant

• Two step analytic procedure

• Package of group differences: an experiment with 3+ groups that can be thought of as a

package of two-group tests

o With three groups, there are three pairs of mean differences: µ1 vs. µ2, µ2 vs. µ3, µ3

vs. µ1 With four groups, there are six pairs, etc.

ANOVA Procedure

• First step: examines whether any of the group means differ

o If overall test is significant, we use t tests to examine specific group differences

Hypothesis

• Null hypothesis of no effect predicts that group means are identical in population

o H0: µ1 = µ2 = µ3

o The alternate hypothesis states that at least one pair of means differs

find more resources at oneclass.com

find more resources at oneclass.com

## Document Summary

Paired-samples t-test: appropriate for within-group designs with two measurements, outcome variable must be continuous. Difference (change) scores: the paired-samples t test requires two scores per individual (pretest and posttest, hypotheses and computations involve difference scores that subtract the two variables, diff = x2 - x1 = posttest - pretest. If increase from pre --> post then positive. If decrease from pre --> post then negative. Null hypothesis: vast majority of pretest-posttest designs specify a null hypothesis of no change, states that the mean different or change in the full population is zero, h(cid:1004): _diff = (cid:1004) Alternate hypothesis: what kind of effect can we expect to see, requires a two-tailed p-value. One- factor anova: appropriate for research scenarios with a categorical independent variable and one numeric (continuous) dependent variable. Independent-samples t test was used to compare means of two groups: one-factor = one independent variable, anova is appropriate for between-group designs with two or more groups.