psych stats exam 3

what does an ANOVA measure?

1) used to determine if the means of 2+ groups significantly vary 2) the larger the differences are for between-groups means, the larger the variance will be 3) if group means are equal, then the variance of group means is equal to 0 4) if 2 groups, you can use a t-test or ANOVA

For a one-way between-subjects ANOVA comparing two treatment conditions with a sample of n = 10 in each treatment, which of the following identifies the correct df for the F‐ratio?

1, 18

A researcher conducts a one-independent sample t-test with a sample of 12 participants. What are the degrees of freedom for this hypothesis test?

11

For a one-tailed t-test using an alpha of .01, what would be the critical t- value for a sample of n = 30?

2.462

An analysis of variances produces dfb = 3 and dfw = 24. For this analysis, what is the dft?

27

What are the degrees of freedom numerator for a study with n = 12 in each of four groups?

3

An analysis of variance produces SSt = 40 and SSw = 10. For this analysis, what is SSb?

30

In a two-way between subjects ANOVA, how many total sources of variation are there?

4

What is the effect of a large value for the estimated standard error?

A smaller value of t

Why do we make the transition from using z-tests to using t-test?

Because most of the time the population variance is unknown. We have to know this information to use a z-statistic. The t-statistic substitutes sample variance for population variance.

A researcher computes a 4 × 4 between-subjects ANOVA and finds two significant main effects and a significant interaction. What is the next appropriate step?

Compute simple main effect tests for the interaction.

The t-statistic is an inferential statistic used to determine the number of standard deviations in a t-distribution that a sample mean deviates from:

a population mean or mean difference stated in the null hypothesis

A simple main effect test is appropriate for analyzing which significant result?

a significant interaction

Simple main effect tests are necessary to analyze:

a significant interaction

A main effect is a source of variation associated with mean differences:

across the levels of a single factor

estimated standard error

an estimate of the standard deviation of a sampling distribution of sample means selected from a population with unknown variance; it is an estimate of the standard error or standard distance that sample means deviate from the value of the population mean stated in the null hypothesis

degrees of freedom within groups

associated with the error variance in the denominator (N-k)

degrees of freedom between groups

associated with the variance of group means in the numerator (k-1)

n (ANOVA)

number of scores in each treatment when n is constant for all conditions, N = k * n

sources of variation for 2-way ANOVA

one source = error variation three sources = b/w-groups variation

You read about a study testing whether night shift workers sleep the recommended 8 hours per day. Assuming that the population variance of sleep is unknown, what type of test is appropriate for this study?

one-independent sample t-test

limitation of t-tests

restricted to comparing only 2 groups

In a two-way between-subjects ANOVA, which effect is potentially the most informative when it is significant?

the interaction

There are ____ factors in a 2 × 3 ANOVA design.

2

A researcher reports that alertness in the classroom varies by the intensity of lighting in the room, F(3, 36) = 3.96, p < .05. How many light intensity groups were observed in this study?

4

What is the critical value for a study with n = 12 in each of two groups at a .05 level of significance?

4.30

A researcher conducts a two-independent sample t-test. What are the critical values for a two-tailed hypothesis test at a .05 level of significance when n = 14 participants in each group?

+2.056 and -2.056

How many interactions are possible in a two-way between-subjects ANOVA?

1

8 possible outcomes of 2-way ANOVA

1) all 3 hypothesis tests aren't significant 2) significant main effect of factor A only 3) significant main effect of factor B only 4) significant main effect of factor A and factor B 5) significant A*B interaction only 6) significant main effect of factor A and A*B interaction 7) significant main effect of factor B and A*B interaction 8) all 3 hypothesis tests are significant

steps to compute post-hoc test

1) compute test statistic for each pair of group means 2) compute critical value for each pairwise comparison 3) make decision to retain or reject null hypothesis

assumptions of one-independent sample t-tests

1) normality: data in the population being sampled are normally distributed 2) random sampling: data we measure were obtained from a sample that was selected using a random sampling procedure 3) independence: probabilities of each measured outcome in the study are independent

graphing an interaction interpretations

1) when 2 lines are parallel, this indicates that a significant interaction isn't likely 2) when 2 lines touch or cross, this indicates that there is a possible significant interaction

A researcher computes a significant one-way between-subjects ANOVA with eight participants in each of four groups and MSw = 18.1 and dfw = 30. What is the critical value for Tukey's HSD at a .05 level of significance for each pairwise comparison?

5.8

There are ____ cells in a 2 × 3 ANOVA design.

6

A researcher reports that emotional responses varied by the type of stressor in a controlled environment, F(4, 55) = 6.01, p < .05. How many participants were observed in this study?

60

An analysis of variance produces SSb = 30 & MSb = 5. In this analysis, how many groups are being compared?

7

If both samples in the last example have n = 10, the two-independent sample t-statistic will have df = 19.

FALSE

The results of a hypothesis test are reported as follows: t(21) = 2.38,p < .05. What was the statistical decision and how big was the sample?

The null hypothesis was rejected using a sample of n = 22

Margo wants to compare a group of women to a group of men to see if women are better listeners. What is the best statistic for this study?

Two-independent sample t-test

Why does the t-distribution have greater variability in the tails of the distribution compared to a normal distribution?

because the sample variance is substituted for the population variance to estimate the standard error in this distribution

Which of the following is a source of variation in the one-way between-subjects ANOVA?

between-groups variation

The source of variation that cannot be attributed to or caused by having different groups is called:

both a and b within-groups variation error variation

F-distribution

both the numerator and denominator must be positive values; range from 0 to positive infinity; rejection region is in the positive tail; ONE-TAILED

cell

combination of one level from each factor n = number of participants per cell or group N = total number of participants in study

simple main effect tests

compares the mean difference of one factor at each level of the second factor then conduct post hoc tests on any significant simple main effects that are found

levels of the factor

conditions or values that make up the factor; the number of groups or different ways a variable is observed

The two-independent sample t-test can be only computed when:

different participants are observed one time in each group

validity

extent to which we measure what we say we are measuring

factor

independent variable - designates the groups being compared

A source of variation associated with the variance of group means across the combination of levels of two factors is called a:

interaction

When researchers plotted the cell means of their data, they found that the lines of the graph crossed. This means that they likely found a:

interaction

k (ANOVA)

number of levels of a factor or the number of groups

main effects

source of variation associated with mean differences across levels of a single factor

interaction

source of variation associated with variance of group means across a combination of levels of 2 factors measure of how cell means at each level of one factor change across levels of the 2nd factor (A*B)

two-independent sample t-test

statistical procedure used to test hypotheses concerning the difference between 2 population means, where variance in 1 or both of the populations is unknown

one-independent sample t-test

statistical procedure used to test hypotheses concerning the mean in a single population with an unknown variance

t statistic

substitutes population variance with sample variance in standard error formula inferential statistic used to determine the number of standard deviations in a t-distribution that the sample mean deviates from the mean stated in the null hypothesis

F-statistic

test statistic for ANOVA

two-way ANOVA

tests hypotheses concerning variance of groups created by combining levels of 2 factors

one-way between-subjects ANOVA

tests only one factor; different participants are observed at each level of a factor

To report the results of a t-test, which of the following is not reported?

the critical values

A researcher compares the mean difference between two groups with 15 students in each group and reports the following result for a two-independent sample t-test: t(29) = 3.52, p < .05. If this is a two-tailed test at a .05 level of significance, then what MUST be incorrect with this result?

the degrees of freedom

For an analysis of variance, the term "two-way" refers to

the number of factors in the design

degrees of freedom

the number of scores in a sample that are free to vary (n-1) as the sample size increases, the degrees of freedom increase and the tails get closer to the x axis

In a sample of 26 participants, a researcher reports the following result for a one-independent sample t-test: t(25) = 1.907, p < .05. If this is a two-tailed test at a .05 level of significance, then what MUST be incorrect with this result?

the p value

What is the primary difference between a z-test and a t-test?

the population variance is unknown in a t-test

The two-way ANOVA differs from the one-way ANOVA in that:

the two-way ANVOA is used when we observe the levels of two factors

Homogeneity of variance refers to the assumption that:

the variance of scores in each population is equal

N (ANOVA)

total number of scores in a study

The one-way between-subjects ANOVA is used when different participants are assigned to group(s).

two or more

results must have...

value of the mean, test statistic, degrees of freedom, p value, and significance (APA style)

within-groups variation 2-way ANOVA

variation associated with the differences in participant scores within each group placed in denominator

between-groups variation

variation attributed to the mean difference between groups (numerator) ** want this value to be large

within-groups variation

variation attributed to the mean differences within each group (denominator) ** error variation (want small value)

A researcher reports the following result for a t-test at a .05 level of significance: t(40) = 3.02, p < .05. Is this result significant?

yes, for both a one- or a two-independent sample t-test

What are the two sources of variation in a one-way ANOVA? What is the difference between the two?

• Between-groups Variation: variation attributed to mean differences between groups ▫ We want this to be big- we are conducting the test because we think that a difference exists • Within-groups Variation: variation attributed to mean differences within each group ▫ This is error variation▫ We want this to be small

Identify the Factor and Levels: Does the time of day one takes a class affect the final grade in the class? We test 3 groups of participants who are in either an 8:00am class, 12:30pm class, or 4:00pm class.

• Factor = time of day • Levels = 8:00am, 12:30pm, 4:00pm

For an ANOVA, identify what each of these notations mean: K, n, N

• K = number of levels of the factor • n = number of scores in each treatment • N = total number of scores in the study

What is the difference between a main effect and an interaction?

• Main Effect: a source of variation associated with mean differences across the levels of a single factor • Interaction: a source of variation associated with the variance of group means across the combination of levels of two factors; a measure of how cell means at each level of one factor change across the levels of a second factor

If you get a significant one-way ANOVA, what is the next step and what is the purpose of this next step?

• Next step = post hoc test • Purpose = to determine which pair or pairs of group means significantly differ

What is the difference between a one- independent sample t-test, a two- independent sample t-test, and a one- way ANOVA?

• One-independent sample: test hypotheses concerning the mean in a single population with an unknown variance • Two-independent sample: test hypotheses concerning the difference between two population means • One-way ANOVA: test hypotheses concerning the difference between two or more population means

How does the shape of a t-distribution and F-distribution differ?

• t-distribution: normal distribution • F-distribution: positively skewed