Psych 300B: Test 1 Review (Variability Explained)

What are the 4 ways we can test the credibility of our results

1. Hypothesis testing

2. Effect size and power

3. Replication

4. Proportion of variability explained (r²)

How do we test the credibility of our results using hypothesis testing

Look at if p(obs) < p(a) where p(obs) = actual probability of making a type 1 error

How do we test the credibility of our results using effect size and power

Look at if treatment affected participants behaviour and use sample data to infer behaviour in population

How do we test the credibility of our results using replication

We repeat a study to see if we get the same result

What is the proportion of variability explained

It is the degree to which treatment (IV) affected the participants behaviour (DV)

it is the strength between the two variables

What is the major problem with hypothesis testing

There is always a possibility of the event occurring by chance, even if p(obs) = 0.01

What does a hypothesis test actually tell us

The probability of observing an event due to chance

What 2 things does a hypothesis test fail to tell us

1. How strongly our treatment of participants is related to their change in performance

2. How much of a treatment effect exists

Explained variability

r² is a measure of the strength of a relationship between two independent variables

It is the proportion of variability accounted for

What will r² always fall between

0 and 1, sometimes referred to coefficient of determination

What do r, r², r²(100) and (1 - r²) actually mean

r → measure of association between X and Y

r² → proportion of variability in Y explained by variability in X

r²(100) → % of variability in Y accounted for by variability in X

1 - r² → unexplained variability (change in particpants behaviour not explained by treatment)

What are the two ways that we can compute r²

1. Compute point-biserial correlation r_pb

2. Convert t-scores into r²

T or F: Since df is in the denominator of the equation to calculate r², an increase in n will lead to r² decreasing

F, t increases along with n as well, (since se is getting smaller)

How should one calculate r²

By using the equation using your calculated t score

Why should r² not be calculated in a related samples design

Because r² measures the proportion of variance between two independent levels of an IV, but a related samples design only has one value (D-bar)

What is required to report r² for independent samples design

Must have k = 2

What does r² tell us about the IV in a related samples design

Nothing, it only tells us the relationship before and after condition (relationship between X and Y)

Given se = 1.3, t(16) = 1.54, p > .10 and r² = .13, how do we report this in an APA way

… se = 1.30, t(16) = 1.54, p > .01, r² = .13

or

… “13% of the variability in (name the DV … behaviour) is associated with (name your IV), but 87% of the variability in (name the DV) is unaccounted for”

What is a small, medium and large effect of r²

Small - r² = .10

Medium - r² = .25

Large - r² = .40

All things being equal, what is the effect of increasing the sample size n in a study with regard to rejecting the null and credibility

Increases the probability of rejecting the null, but decreases the credibility of the study

In an independent samples design we report ____, for multi group designs (ANOVA) we report ____

r² for independent samples design

R² for multi group designs

What does r² tell us when calculated by squaring r in a related samples design

Proportion of variability between X and Y, but nothing about the effect of IV