Quantitative Methods in Psychology (CONCEPTUAL EXAM #2)

Formula for Pearson's r

∑(Zx)(Zy)/N --> the sum of multiplied pairs of Z scores divided by the number of pairs

Definition for Person's r

When both the independent variable and the dependent variable are interval ratio, r is a measure of the strength and direction of their association

What is Pearson's r range and what does the value tell us?

Pearson's r ranges from -1.0 to 1.0

Absolute value (0.0 and 1.0) tells us the strength of the relationship between the two variables, but the SIGN (+/-) tells us the direction of the relationship

When r is negative there is an __________ between the two variables.

"When one variable goes ____, the other goes ______."

inverse relationship; up, down

When r is positive there is an __________ between the two variables.

"When one variable goes ____, the other goes ______."

positive relationship; up, up

Coefficient of determination

R^2

What does the coefficient of determination tell us?

It tells us what proportion of variance in Y is accounted for by variance in X.

So, if r =.7, then R^2= .49

Therefore, we can say "49% of the information about Y is contained in X.

It's basically effect size!

Degrees of freedom for critical z in Pearson's r

df = # of pairs of scores - 2

Formula for Fisher's Z

Z = (z1 - z2) / (sqrt1/N1-3 +1/N2-3)

Definition for Fisher's Z

used to establish whether two Pearson's r correlations from separate and unmatched samples differ significantly from one another

*done by converting Pearson r values into Fisher's z, then applying the z-test

Null hypothesis for Fisher's Z

H0 = the two sample correlations represent a common population correlation

What happens to our test statistic for Fisher's z when we increase the sample size?

When the sample size is increased, the test statistic also increases! Therefore, the likelihood that we will reject the null also increases

Paired samples t-test is aka...

dependent t-test; correlated samples t-test

Paired samples t-test used when...

a researcher wants to evaluate the difference between the MEAN of TWO GROUPS using data from a single sample

Samples in a paired samples t-test are often comprised of data from...

the same subjects! usually under pre and post experiments. However, you might have 2 people who are so similar that they are matched

In paired samples t-tests, when r is positive, the denominator gets...

smaller! which makes the t value larger, therefore the probability of rejecting the null hypothesis increases

null hypothesis of paired samples t-test

H0 = the true mean difference between the paired samples is zero

H0=m1=m2

Definition for 1 way anova

used on interval data when more than two sample means are being compared for differences

Definition for F ratio (used in 1 way and factorial anova)

determines the ratio between the variability occurring between the sample groups and the variability occurring within the sample groups

The higher the f value, the higher the likelihood...

that the samples represent different populations (indicated high variability between groups, lower variability within groups)

A significant F ratio ONLY tells us that there are significant differences among the _________, once you reject the null, you have to calculate _________, which tells you _______ these differences occur

group means; Tukey's HSD; where

degrees of freedom between for 1 way anova

K (the number of columns) - 1

degrees of freedom within for 1 way anova

N-K (the number of columns)

Definition of factorial anova

compares means across two or more independent variables; assessing main effect and interaction effect

Main effects in factorial anovas assess...

whether either of the single independent variables have effects on their own

Interaction effects in factorial anovas assess...

whether the two independent variables have an effect in concert with one another

formula for fancy n^2 =

SSbetween/(SSbetween+SSwithin)

If the within group variability is small, then the separate sample groups are most likely to have ________ distributions

leptokurtic

True/False: The F ratio is a nondirectional, two-tail test of differences among sample group used whenever the data is in interval form

true!

True/False: ANOVA demands that AT LEAST four sample groups must be compared

false! at least THREE groups

True/False: On a four group design, the between degrees of freedom for a one-way ANOVA must equal 4

false! they would equal 3

True/False: ANOVA assumes that the data are at least interval

true!

True/False: Assuming that the mean differences and standard deviations are constant, you are more likely to reject the null hypothesis when using a paired-samples t-test than an independent samples t-test

true!

True/False: For an independent samples t-test and a paired samples t-test with same number of subjects, the degrees of freedom would be the same

false!

True/False: In a 1-way ANOVA, if the sum of squares between remains constant and the number of means being compared decreases, you are more likely to find a significant difference among the means.

true!

If the F statistic is significant in the 1-way ANOVA, the next step to take would be

A. to accept the null hypothesis and conduct a post-hoc test

B. to reject the null hypothesis and conduct a post-hoc test

C. to report the result and reject the null hypothesis.

D. to report the result and accept the null hypothesis

B

If the Pearson's r between variables X and Y is -.40, how much of variance in Y can be predicted by X?

A. 40%

B. 25%

C. 16%

D. none - negative correlations do not permit you to explain variance in a criterion variable

C

In a factorial ANOVA, when neither main effect is significant, the interaction cannot be significant.

false!

True/False: In an ANOVA, only the size of the sample influences the degrees of freedom within.

false!

In a one-way ANOVA, as the sum of squares between increases, the probability of accepting the null hypothesis

A. decreases

B. increases

C. remains constant

D. you cannot tell because the degrees of freedom within changes depending on the value of the sum of squares within.

A

In a study where type of reading training (whole language vs. phonics) and length of training (6 weeks vs. 12 weeks) were examined for their effect on reading test scores, the scores improved only for children in the phonics training for 12 weeks. This would be described as a(n)

A. main effect for type training and a main effect of length of training

B. interaction between type of training and reading test scores

C. interaction between length of training and reading test scores

D. interaction between type of training and length of training

E. all of the above

F. none of the above

D

True/False: In an ANOVA, the greater the variability between each cell mean and the scores within that cell, the greater the SS between.

false!

True/False: The reason there is only one number shown for degrees of freedom in any t-test is because the degrees of freedom between must always be 2.

false!

In an experiment, the numerator in the F statistic is a measure of

A. the effect of the independent variable on the dependent variable

B. the effect of individual differences among subjects on the dependent variable

C. the effect of the number of subjects on the dependent variable

D. the effect of the dependent variable on the independent variable

A

In the F statistic, which of the following does NOT influence the MS within?

A. variation between each cell mean and the scores in that cell

B. the number of groups (or means being compared) in the study

C. differences between each group mean and the grand mean

D. all of the above influence the MS within

C

True/False: With respect to a factorial ANOVA, if both main effects are significant, the interaction must also be significant.

false!

The term -2r(SEM1)(SEM2) in the paired samples t-test causes the t-ratio to be ________ than it would if the term were excluded.

A. smaller

B. larger

C. less biased with respect to the population parameter

D. more biased with respect to the population parameter

B

When you have one independent variable with more than two levels, and the DV is interval-ratio, which statistical test should be used?

A. factorial ANOVA

B. independent samples t

C. Pearson's r

D. 1-way ANOVA.

D

Which of the following, if any, is false with respect to Pearson's r?

A. Both of the variables must be interval/ratio

B. The ranges of values for x and y should NOT be restricted

C. The form of the relationship between X and Y must be linear

D. All of the above are false

D

Why do we conduct a post-hoc test if we find a significant F in a one-way ANOVA?

A. Because smaller sample sizes are less likely to yield significant differences, and each group is a smaller sample than the total N.

B. Because the book and Prof. Kilianski told us to.

C. Because the sum of squares within underestimates the population sum of squares

D. Because you don't know which means differ from which other ones when there are more than two of them.

D

Why is the term 2r(SEM1)(SEM2) not included in the independent samples t-test?

A. Because the relationship in an independent samples t-test is assumed to be non-linear

B. Because the r is assumed to be 0 in the independent samples t-test

C. Because the denominator in the independent samples t-test underestimates the estimated standard error the difference

D. Because we only use SEM1 in the independent samples t-test

B

With respect to the paired-samples t-test, as the size of the r decreases, the t-ratio _____ making it ________ to reject the null hypothesis.

A. decreases; less likely

B. increases; more likely

C. increases; less likely

D. remains the same; equally likely

A

MS =

SS/df

F =

MS/MSw