Psych Stats 308 Exam 2

Which of the following is a similarity between the single sample z-test and single sample t-test?

They both are for comparing your sample to a known population.

In what situation should you use a single sample t-test instead of a single sample z-test?

When the population standard deviation is unknown.

In what situations should you use a paired samples t-test instead of a single sample t-test?

When you want to study change across two time points.

What is the underlying logic of the single sample t-test?

We are trying to figure out the probability of getting our sample mean, with our sample size, from the null hypothesis population.

What is the underlying logic of a paired samples t-test?

We are trying to figure out the probability of getting our sample mean difference, with our sample size, from the null hypothesis population.

How do the t-test formulas compare to the z-test formulas?

The t-test formulas use SD in place of σ

How do we alter the formula for the sample standard deviation to make it an unbiased estimate of the population standard deviation?

Divide by N-1 instead of N

Where does the mean of the null hypothesis population typically come from for a paired samples t-test for analyzing change?

It is assumed to be zero based on the null hypothesis that there is no change.

What is the sampling distribution for the single sample t-test made up of?

All possible means from samples of a given sample size from the null hypothesis population.

What is the standard error of the sampling distribution for a a single sample t-test?

It is the average distance sample means in the sampling distribution are from the mean of the null hypothesis population.

What is the sampling distribution for paired samples t-test made up of?

All possible means of change scores from samples of a given sample size, drawn from the null hypothesis population (where there is on average no change).

What is the standard error of the sampling distriubtion for a paired samples t-test?

It is the average distance sample means of change scores in the sampling distribution are from the mean of the null hypothesis population (which is typically zero).

Suppose a researcher gets a result of t=-2.50. Which of the following is NOT a valid interpretation of these results?

There is a large effect, because the mean of the alternative hypothesis population is 2.50 sd below the man of the null hypothesis population.

Which of the following is true regarding the relationship between t-scores and p-values?

They are inversely related (if one is larger, the other is smaller, and vice versa)

When you reject the null hypothesis in a single sample t-test, how do you statistically interpret the results?

There is less than a 5% chance of getting your sample mean, with a sample of your size from the null hypothesis population.

When you retain the null hypothesis in a paired samples t-test, how do you statistically interpret the results?

There is greater than a 5% chance of getting your sample mean difference, with a sample of your size, from the null hypothesis population where there is no change.

When you reject the null hypothesis in a paired samples t-test, how do you statistically interpret the results?

There is less than a 5% chance of getting your sample mean difference, with a sample of your size, from the null hypothesis population where there is no change.

Which of the following yields more power in a single sample t-test or paired samples t-test?

The sample size is larger.

As sample size increases (say from 50 to 100), which of the following is true regarding the t-critical for t-tests?

It gets smaller (i.e., decreases towards 1.96)

Which of the following is an accurate interpretation of p=.02 for a single sample t-test?

There is a 2% chance of getting that sample mean, with that sample size, from the null hypothesis population.

What is the interpretation of a Cohen's d of 2.00.

The alternative hypothesis population mean is two standard deviations above the null hypothesis population mean.

Which of the following leads to a larger Cohen's d effect size?

Larger difference between sample and population mean

If a paired samples t-test is statistically signficant (p < .05), which of the following will also be true regarding the confidence interval?

It will not contain the mean of the null population, which is typically 0

Degrees of freedom (t-test)

Degrees of freedom are the number of data points that are free to vary

T-distribution

all the possible means of a given sample size drawn from the null population, contingent on the degrees of freedom

Distribution of means (paired samples t-test)

all possible mean differences of given sample size drawn from the null hypothesis population where there is zero average difference

standard error (paired samples t-test)

average distance mean differences are from zero in units of standard deviation

t-critical

the value that marks the boundary for your statistical decision in a t test.

Which of the following is in common between single sample, paired samples, and independent samples t-tests?

They all involve analysis of means

What is the structure of the data for an independent samples t-test

2 groups of people at 1 occasion

What kinds of variables are needed to run independent samples t-tests?

A nominal variable and an ordinal or ratio/interval variable

What kinds of research questions are independent samples t-test used to answer?

Research questions that involve comparing two groups.

What is the unit of analysis for independent samples t-tests?

Mean differences

Which of the following possible studies of relationship satisfaction among newlyweds is most likely to. involve an independent t-test?

Researchers compared relationship satisfaction between newlyweds who took a relationship education course and those who did. not take the course

What is the underlying logic of the independent samples t-test?

We are trying to figure out the probability of getting our two samples, of our sample sizes, if the null is true (i.e.,, they came from the same population)

What does the typical null hypothesis look like for an independent samples t-test?

The groups are not different

What does the typical alternative hypothesis look like for an independent samples t-test?

one group is lower/higher than the other group

Which of the following is typically true for the mean of the sampling distribution for an independent samples t-test?

It is assumed to be zero because if the null hypothesis is true, on average there will be no difference between two samples from the same population

What is the sampling distribution for the independent samples t-test made up of?

All possible differences between means from two samples, of two given sample sizes, drawn from the same population.

What is the standard error of the sampling distribution for an independent samples t-test?

It is the average distance of our differences between means are from zero

What do the top and bottom of the t-test formula for the independent samples t-test represent?

The difference between means you got in your data over the difference between means you might expect to get if the null hypothesis were true.

Which of the following is NOT a valid interpretation of t-scores in an independent samples t-test?

they directly correspond to the p-value, so larger t-scores mean larger p-values.

When you retain the null hypothesis in an independent samples t-test, how do you statistically interpret the results?

There is greater than a 5% chance of getting your size of difference between means, with your two sample sizes, if the null hypothesis is true

When you reject the null hypothesis in an independent samples t-test, how d you statistically interpret the results?

There is less than a 5% chance of getting your size of difference between means, with your two sample sizes, if the null hypothesis were true (i.e., your means came from the same population)

Which of the following yields more power for an independent sample t-test?

A larger difference between means

how is effect size Cohen's d interpreted for indepednent samples t-tests?

It is an estimate of the distance between the means of the two populations, assuming the alternative hypothesis is true.

How are 95% confidence intervals interpreted for independent samples t-tests?

With repeated sampling, 95% of the time the three difference between population means will lie within that interval.

Distribution of differences between means (independent samples t-test)

The distribution of differences between means is all the possible differences between means, of samples of those two sizes, drawn from the same null population

Standard error (for independent samples t-test)

The standard error for independent samples t-test is the average distance the difference between means are from zero, in standard deviation units.

Cohen's d

(ind. samples t-test) is the difference sample means are from each other in units of standard devation.

Confidence intervals (ind. samples t-test)

an estimation for how sure we are about our mean differences in retaining or rejecting the null given our sample means

Power (ind. samples t-test)

probability of rejecting the null hypothesis if the alternative hypothesis is true

What types of research questions do one-way ANOVAs address?

Questions about how two or more groups vary on some ordinal/ratio outcome.

What kind of data are needed for one-way ANOVAs?

A nominal group variable (or IV) and an ordinal/ratio outcome variable (for DV)

What is the unit of analysis for ANOVAs?

Variance of means

Suppose a researcher wanted to study math skills. Which of the following sounds like a null hypothesis for ANOVA?

Math scores will not vary significantly across ethnicity.

What does the typical alternative hypothesis look like in ANOVA?

The outcome varies across your groups

If you have more than two groups in your data, why is it typically recommended that you do a single ANOVA rather than multiple independent samples t-tests?

If you do multiple tests, your chance of Type I error will be more than 5%

What is the logic of ANOVA?

We are trying to figure out the likelihood of getting means that vary as much as ours do (with samples of our sample sizes) if drawing them all from the same population.

In ANVOAs, which number tells us how much our means vary?

between-groups variance

Which number tells us how much we expect our means to vary by chance, if the null is true, and they all come from the same population?

within-groups variance

What is the general logic of the f-ratio?

How much our group means vary/how much we expect OUR group means to vary by chance given the null hypothesis that they are all from one population

What is the sampling distribution in ANOVA made up of?

All possible f-ratios you could get, with your number of groups and your sample sizes, if drawing your samples from the same population

What does the f-distribution look like?

one tailed test, skewed to the right, starting with 0 and with the mode being 1

How do you interpret rejecting the null in an ANOVA?

There is less than a 5% chance of getting an f-ratio as large as yours if the null hypothesis is true and your groups all came from the same population

How do you interpret retaining the null in an ANOVA?

There is greater than a 5% chance of getting an f-ratio as large as yours if the null hypothesis is true and your groups all came from the same population

Alpha inflation

alpha inflation is that the chance of type I errors goes up with each hypothesis test

between groups variance

between groups variance tells us how much our means vary, but without comparison, it can be difficult to tell if it is due to sampling error or due to an effect

within groups variance

an indicator of sampling error

f-ratio

between groups variance/ the within groups variance

f distribution

is all the possible f-ratios of our samples sizes drawn from the same null population. There is no standard error, as it is a one-tailed, skewed distribution

Which of the following do you learn from the f-test in ANOVA?

Whether or not the DV varies significantly across the IV

Which of the following is NOT a limitation of the f-test in anova?

It doesn't tell you whether or not the IV (group variable) is significantly related to the DV (outcome variable)

Which of the following do you learn from the pairwise comparisons?

Whether or not the differences between particular pairs of groups are signficant

Which of the following do you learn from r-squared?

the proportion of variance in the DV accounted for by the IV

Which of the following is true?

F-test and pairwise comparisons are hypothesis tests/ r-squared and cohen's d are corresponding effect sizes

which of the following is true?

r-squared is the effect size corresponding to the f-test, and cohen's d is the effect size corresponding to the pairwise comparisons

what is the logic of the f-test in anova?

we are trying to figure out the likelihood of getting means that vary as much as ours do (with samples of our sampel sizes), if drawing them all from the same population

What is the logic of pairwise comparisons in ANOVA?

we are trying to figure out the likelihood of getting this large of a difference between two means, with our sample sizes, if drawing them from the same population

What is the typical process for running an ANOVA with pairwise comparisons?

Run the f-test, and then if it is statistically significant, run the pairwise comparisons

IF you run an ANOVA with four IV groups and get a statistically significant f-ratio, which of the following scenarios might be your minimal expectation?

the pairwise comparisons of the outer groups (the groups with the lowest and highest means) will be signficant

What are key differences between the f-test and pairwise comparisons?

the f-test assesses variances across all group means, while the pairwise comparisons assess differences between two of the means.

which of the following is NOT a difference between the f-test and r-squared

r-squared has with-groups variance on the bottom (so it is a ratio), while the f-test has total variance on the bottom (so it is a proportion)

how would you interpret r squared= .25

the IV accounted for 25% of the variance in the DV, and it is a large effect

which of the following is true regarding power in ANOVA?

even if the f-test is sufficiently powered, some of the pairwise comparisons still might not be sufficiently powered

which of the following do not influence the power of the f-test in ANOVA?

one tailed vs two tailed tests

what confidence intervals are we typically interested in for ANOVA?

CIs around the estimates of group means and CIs around the differences between pairs of means

Which ANOVA extension allows for the analysis of change over time across two or more occasions?

Repeated measures ANOVA

Which ANOVA extension involves a single IV and multiple DVs?

MANOVA

Which ANOVA extension involves multiple IVs?

Factorial ANOVA

r-squared

r-squared is the effect size that goes with f-test. it tells how much the outcome varies across groups

MANOVA

MANOVA is multiple one-way ANOVA tests combined

Factorial ANOVA

multiple IVs and their interactions

Repeated measures ANOVA

when the independent variables are actually in waves