RUTGERS quantitative methods in psych conceptual exam 2 (kilianski)

Correlation Coefficient (r)

ranges from -1 to 1

both variables must be interval/ratio level

anticipated relationship must be linear

homoscedasticity (relationship between x and y is constant from top to bottom) is assumed

range of values is not restricted

The negative/positive sign indicates the direction of the relationship (when r is positive, one variable increases as the other increases; when r is negative, one variable increases as the other decreases)

r of 0 means the two variables are unrelated—the value of one tells you nothing about the value of the other; r of 1 or -1 means the values fall along a straight line

With lower absolute values of r, we lose predictive accuracy

positive correlation - x goes up and y goes up (direct relationship)

negative correlation -x goes down and y goes up (inverse relationship)

values of r

values range from -1 to 1; 0 means no correlation

Pearson's r

finds correlation between IV and DV (relationship between DV and IV is expected to be linear)

need to find the cross product of the z scores to find Pearson's r

the bigger the r the smaller the denominator

Pearson's r null hypothesis

Ho: r(population) = 0

In a Pearson's r test, there is no restriction between of range within the range of possible values.

true

In a Pearson's r test, a significant correlation means there is a causal relationship between the IV and DV.

false

Coefficient of determination

r squared; effect size in a Pearson's r test; tells you what percent of the variability in the DV is accounted for by the IV

Fishers z

The Fisher Z-Transformation is a way to transform the sampling distribution of Pearson's r (i.e. the correlation coefficient) so that it becomes normally distributed. The "z" in Fisher Z stands for a z-score.

Fisher's z' is used to find confidence intervals for both r and differences between correlations. But it's probably most commonly be used to test the significance of the difference between two correlation coefficients, r1 and r2 from independent samples.

Paired Samples t-test

used for repeated measures in experiments; DV is measured, experimental manipulation is administered, DV is measured again

purpose is to find difference between two means

use the SAME people (before/after manipulation)

how increase/decrease in r values affect t in paired samples t-test

r increases t increases, r decreases t decreases

SD increases (numerator)

t decreases

null hypothesis

t=0

z=0

f=1

r population=0

SSw increases

f decreases

SSb increases

f increases

dfb increases

f increases

dfw increases

f increases

large f ratio

mean square bw is larger than mean square within, variability between the group is larger than variability occuring the groups

When retesting subjects, an independent samples t-test is not acceptable because scores within subjects are correlated.

true

Why is the SEd different in a paired samples t-test than an independent sample?

we must take within-subjects correlation into account (if significant)

one-way ANOVA test

finding differences between three or more sample means; finds ratio of variability between and within groups

looks at variance in the DV and what its sources are

From an overall F-test, we do NOT know where the specific mean differences are, so we must perform a follow-up test of Tukey's HSD

one-way analysis of variance (ANOVA) null hypothesis

Ho: μ1 = μ2 = μ3...

In finding the difference between three or more means, you cannot use multiple t-tests because the probability of falsely accepting the null hypothesis increases with each test.

false; more likely to falsely reject the null hypothesis

Tukey's HSD

used when there is a significant difference to find the specific mean difference; only used in a one-way ANOVA or a factorial ANOVA for every significant F with three or more levels

SS(w) means square within

find the mean for each level of the IV; subtract it from each individual score; square those differences; sum the squares; add the values together

Level of a IV refers to how many groups/conditions there are

SS(b) mean square between

find each condition mean; subtract the grand mean from each condition mean; square these differences; multiply them by the sample size for that condition; add those values together

The bigger the differences between conditions are, the bigger the sum of squares between will be.

true

factorial analysis of variance (ANOVA)

compares means across two or more IVs

DV must be interval/ratio

Explores the effects of each IV separately (i.e., main effects) and different combinations of IVs (i.e., interactions) (The significance of one (i.e., a main effect or interaction) does NOT depend

on the significance of another)

"main effect" in a factorial ANOVA

effects of IVs seperately

"interaction" in a factorial ANOVA

effects of different combinations of IVs

2 x 2 ANOVA

two IVs with two levels each

2 x 3 ANOVA

two IVs, one of which has two levels and one of which has three

When both the independent and dependent variables are interval/ratio level, which statistical test should be used?

Pearson's r

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

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

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.

larger

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

increases; more likely

If the Pearson's r between variables X and Y is -.50, how much of variance in Y can be predicted by X?

25%

Which of the following is used in determining the degrees of freedom between in the F-test?

the number of groups being compared

In the F statistic, the sum of squares between is influenced by

differences between each group mean and the grand mean

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

the effect of the IV on the DV

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

increases

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

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

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

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

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

false

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

true

In an ANOVA, both the number of levels of the independent variable and the size of the sample influence the degrees of freedom within.

true

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 1.

true

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

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

false

In a factorial ANOVA, when neither main effect is significant, the interaction may still be significant.

true

When an ANOVA results in the rejection of the null hypothesis, the between-group variability must be greater than the within-group variability.

true

An interaction can only occur between ___ or more ___ variables

two; independent

In an analysis of variance, total variability results from the accumulated differences between each individual score and the _____.

grand mean

In an analysis of variance, within group variability results from the accumulated differences between each individual score and the ___.

group mean

When a calculated F ratio has a large value, it indicates that the variability between groups is ___ than the variability within groups.

larger

The variance, or mean square, results from diving the sum of squares by ___.

degrees of freedom

mean square

estimates of variance across groups; SS/df

signifies variance in an ANOVA

Type I error

incorrect rejection of a true null hypothesis

When alpha is .05, we have a 5% probability of incorrectly rejecting H0

Type II error

incorrect acceptance of a false null hypothesis

When alpha is .05, we have a 95% probability of incorrectly failing to reject H0

The total sum of squares is made up of two major components, the ___ and the ___.

SS(w); SS(b)

When an ANOVA results in the rejection of the null hypothesis, then the ___ variability must be larger than the ___ variability.

between group; within group

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

leptokurtic

A five-group research design with six subjects in each group has ___ between degrees of freedom and ___ within degrees of freedom.

4; 25

The greater the spread among the various sample means, the larger is the ___ variability.

between group

The F ratio is a non directional, two-tail test of differences among sample groups used whenever the data are in interval form.

true

ANOVA demands that at least four sample groups must be compared.

false

On a four-group design, the between degrees of freedom for a one-way ANOVA must equal 4.

false

ANOVA assumes that the data are at least interval.

true

An F ratio of 5.00 indicates that the variance between groups is five times greater than the variance within groups.

true

The use of the factorial ANOVA is required whenever there is more than one independent variable and the data are in interval form.

true

On a factorial ANOVA, the interaction effect will always be significant if the main effects are themselves significant.

false

To do a factorial ANOVA, there must be a minimum of at least four different treatment conditions.

true

When the obtained value of F is larger than the table value of F for a given number of degrees of freedom, the null hypothesis cannot be rejected.

true

the greater the f statistic, the more likely to reject the null hypothesis

true

One way ANOVA can only be used for numerical data.

true

For pairwise post hoc comparisons, which one of these tests would be considered first choice, because it provides a 95% confidence interval?

Tukey's test

For continuous, normally distributed data with over 3 samples, which one of these tests should be used?

ANOVA

The ANOVA test splits up the variance of the dependent variable into what who groups?

- Between-group variance

- Within-group variance

Which one of these would provide the best visual display of the linear relationship between two numerical variables?

Scatterplot

ANOVA assumes that the data are at least interval.

True

Which one of these tests deals with both continuous and categorical variables?

ANCOVA

ANCOVA is a model with a continuous outcome variables and two or more predictor variables where at least one is continuous and at least one is categorical.

A Pearson r of .90 means the % of information about Y contained in X is roughly 81%.

true

An R^2 of _____ means that the DV cannot be predicted from the the IV.

0

Analysis of Variance involving 2 or more independent variables or predictors

Factorial ANOVA

A sample of n=25 individuals is selected from a population with= 80 and a treatment is administered to the sample. If the treatment is administered to the sample. If the treatment has no effect, then

The same mean should be close to 80 and should lead you to fail to reject the null hypothesis

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

A. Either of the variables must be ordinal

B. The ranges of values for X and Y can be no greater than + or minus 1 SD of their means.

C. The form of the relationship between X and Y can be non-linear

D. None of the above are true

D. None of the above are true

In a 3 x 2 x 2 factorial ANOVA, how many variables and levels are there?

There are 3 variables. The first variable has 3 levels. The second and third variables

have 2 levels each.

After finding a significant F from a one-way ANOVA, what do you know and what do you not know?

You know that there is a difference between your groups, but not what groups specifically differ from each other. (Need Tukeys HSD to determine the specific differences).

What is the dfbetween and dfwithin for F (2, 98) = 3.96, p < .05?

dfbetween = 2, dfwithin = 98

What is the squared amount of variation between each score and the mean of the score's group called?

SSw

If SSbetween is large then you are more/less likely to reject the null?

more

I want to know whether extraversion (extraverted, introverted) and music ability (plays no instruments, plays many instruments) affects the number of tinder matches a person gets. I find that playing instruments while extraverted and introverted predicts more dates. Is this a significant main effect or interaction?

Main effect of music ability

True or false: the smaller the differences are between groups, the bigger the SSb will be.

False

What is the main difference between a one-way and a factorial ANOVA?

A factorial ANOVA has 2 or more IVs.

2 x4 ANOVA has how many null hypotheses?

3

I want to test the effect of drugs (placebo, 1 pill, or 2 pills) and sleep (10hrs, 8hrs, or 6hrs) on depression. What is the type of test will I use?

Factorial ANOVA

What is the F ratio?

The amount of variation between groups/amount of variation within groups

Which pearson's r value indicates a stronger relationship: r = .3 or r = -.6?

-.6

When you have a strong/large correlation between your before and after scores in a repeated measures design (i.e., paired samples t test) does it become easier/harder to reject the null?

Easier (you are more likely to reject the null b/c denominator of paired samples t becomes smaller)

What percentage of the variance is accounted for when you have a significant r = .6?

36% of the variance (use the coefficient of determination = r2 to determine the % of

variance one variable can explain for the other variable)

What is the null hypothesis in a correlation?

The null is that there is NO relationship between the variables; r = 0