Test 3

Which of the following is best to present a structure of a two-factor experiment? Matrix Venn diagram Bar chart Pie chart

Matrix

Obtaining a significant interaction means that both Factor A and Factor B have significant main effects.

false

The null hypothesis for the independent-measures t-test states that there is no difference between the two sample means. (T/F)

false

Two separate samples, each with n = 10 scores, will produce an independent-measures t-statistic with df = 19. (T/F)

false

When pooling variances, the resulting value will be closer to the variance for the sample with the smaller number of scores. (T/F)

false

Computing an independent-samples t-test is appropriate when the population variance is unknown. participants are observed and measured only once. different participants are assigned to each group. All of the above

all of the above

In a two-factor analysis of variance, a main effect is defined as the mean differences among all treatment conditions. mean difference between the two factors. difference between the largest treatment mean and the smallest treatment mean. mean differences among the levels of one factor.

mean differences among the levels of one factor.

A two-factor ANOVA with 2 levels of Factor A and 3 levels of Factor B involves 6 separate hypothesis tests.

False

On average, what value is expected for the F-ratio if the null hypothesis is true? k-1 0 1.00 N-k

1.00

How many separate groups of participants would be needed for an independent-measures two-factor study with 3 levels of Factor A and 4 levels of Factor B? 3 7 4 12

12

A researcher reports t(22) = 5.30, p < .01 for an independent-measures study. How many individuals participated in the study? 21 22 23 24

24

For an independent-measures ANOVA comparing k = 3 treatments with a sample size of n = 5 in each treatment, what is the critical value for the F-ratio using an alpha level of α = .05. 3.49 3.34 3.74 3.88

3.88

A two-factor study with two levels of Factor A and three levels of Factor B uses a separate group of n = 5 participants in each treatment condition. How many participants are needed for the entire study? 30 10 25 5

30

How many separate groups of participants would be needed for an independent-measures two-factor study with 3 levels of Factor A and 3 levels of Factor B? 12 3 9 6

9

What is stated by the alternative hypothesis for an ANOVA? The beta estimate is significant. At least one of the population means is different from another mean. There are no differences between any of the population means. All of the population means are different from each other.

At least one of the population means is different from another mean.

Which of the following describes a typical distribution of F-ratios? Positively skewed with all values greater than or equal to zero Symmetrical with a mean of zero Negatively skewed with all values greater than or equal to zero Symmetrical with a mean equal to df Total

Positively skewed with all values greater than or equal to zero

In analysis of variance, what is measured by the MS values? The total variability for the set of N scores The average distance from one mean to another Population variances Sample variances

Sample Variances

How many separate F-ratios are used in a two-factor ANOVA? Three overall F-ratios One overall F-ratio Two overall F-ratios Four overall F-ratios

Three overall F-ratios

An ANOVA is used to determine whether a significant difference exists between any of the treatment conditions, and post hoc tests are used to determine exactly which treatment means are significantly different.

True

A research design that uses a separate group of participants for each treatment condition is called an independent-measures design or a _____ design. between-subjects within-subjects repeated-measures dependent-measures

between-subjects

Two variables are said to interact when both variables produce a change in the participants' scores. the effect of one independent variable depends on the levels of the second variable. the two variables are differentially influenced by a third variable. both variables are equally influenced by a third factor.

the effect of one independent variable depends on the levels of the second variable.

A researcher predicts that a special training course will be highly effective for females but will have little or no effect for males. This researcher is predicting an interaction between training and gender.

true

For ANOVA, when the null hypothesis is true, the F-ratio is balanced so that the numerator and the denominator are both measuring the same sources of variance.

true

For a hypothesis test with the independent-measures t-statistic, the null hypothesis states that the two population means are the same. (T/F)

true

For a two-factor ANOVA, the significance of any specific F-ratio is completely independent of the significance of the other F-ratios.

true

The percentage of variance accounted for by the treatment effect is usually known as _____ in published reports of ANOVA results. α² μ² σ² η²

η²

Which set of sample characteristics is most likely to produce a significant value for the independent-measures t-statistic? A small mean difference and small sample variances A small mean difference and large sample variances A large mean difference and large sample variances A large mean difference and small sample variances

A large mean difference and small sample variances

Which of the following is an assumption for computing any type of independent-measures t-test? Data in the population being sampled are normally distributed. The probabilities of each measured outcome in a study are independent. Data were obtained from a sample that was selected using a random sampling procedure. All of the above

All of the above

In an analysis of variance, what is a factor? A treatment total An independent (or quasi-independent) variable A dependent variable A treatment mean

An independent (or quasi-independent) variable

Which of the following is an assumption for the two-sample independent-measures t-test, but not the one-sample t-test? Independence Equal variances Random sampling Normality

Equal variances

Which outcome is expected if the null hypothesis is true for an analysis of variance? MS between should be about the same size as MS total SS between should be about the same size as SS total MS between should be about the same size as MS within SS between should be about the same size as SS within

MS between should be about the same size as MS within

In analysis of variance, which value is determined by the size of the sample mean differences? df within SS between SS within df between

SS Between

In a two-sample independent-measures t-test, which of the following is implied by the alternative hypothesis? The difference between the two population means is equal to 0. The difference between the two sample means is equal to 0. The population means are equal to each other. The difference between the two population means is not equal to 0.

The difference between the two population means is not equal to 0.

In a two-factor ANOVA, what is the implication of a significant A x B interaction? Both of the main effects must also be significant. Neither of the two main effects can be significant. The significance of the interaction has no implications for the main effects. At least one of the main effects must also be significant.

The significance of the interaction has no implications for the main effects.

If a two-factor ANOVA produces a statistically significant interaction between Factor A and Factor B, what can you conclude about the main effects for Factor A and Factor B? The significance of the main effects is not related to the significance of the interaction. Either the main effect for Factor A or the main effect for Factor B is also significant. Neither the main effect for Factor A and the main effect for Factor B is also significant. Both the main effect for Factor A and the main effect for Factor B is also significant.

The significance of the main effects is not related to the significance of the interaction.

F-ratios are always greater than or equal to 0.

True

A key difference between a t statistic and a z statistic is that the standard error is _____ to compute a t statistic. estimated placed in the numerator removed replaced

estimated

For an independent-measures t-statistic, the estimated standard error measures how much difference is reasonable to expect between the two sample means if the null hypothesis is true. (T/F)

true

If the results of a two-factor ANOVA show no main effect for Factor A and no significant interaction, then it is safe to conclude that Factor A has no effect on the participants' scores.

true

A one-way ANOVA makes several assumptions. Which of the following is NOT one such assumption? The observations within each sample must be independent. Each group must have the same number of scores or observations (equal ns) The populations from which the samples are selected must be normal. The populations from which the samples are selected must have equal variances (homogeneity of variances).

Each group must have the same number of scores or observations (equal ns)

For an ANOVA comparing three treatment conditions, rejecting the null hypothesis is equivalent to concluding that all three treatment means are different from each other.

False

For an independent-measures t-statistic, what is the effect of increasing the number of scores in the sample? Decrease the likelihood of rejecting the null hypothesis and have little or no effect on measures of effect size. Increase the likelihood of rejecting the null hypothesis and decrease measures of effect size. Increase the likelihood of rejecting the null hypothesis and have little or no effect on measures of effect size. Increase the likelihood of rejecting the null hypothesis and increase measures of effect size.

Increase the likelihood of rejecting the null hypothesis and have little or no effect on measures of effect size.

For the independent-measures t-statistic, what is the effect of increasing the difference between sample means? Decrease the likelihood of rejecting the null hypothesis and decrease measures of effect size. Decrease the likelihood of rejecting the null hypothesis and increase measures of effect size. Increase the likelihood of rejecting the null hypothesis and increase measures of effect size. Increase the likelihood of rejecting the null hypothesis and decrease measures of effect size.

Increase the likelihood of rejecting the null hypothesis and increase measures of effect size.

In general, what factors are most likely to reject the null hypothesis for an ANOVA? Large mean differences and large variances Small mean differences and small variances Large mean differences and small variances Small mean differences and large variances

Large mean differences and small variances

What provides a measure of the variance caused by random, unsystematic differences? SS Total The error term df Within The F ratio

The error term

If the results of a two-factor experiment are presented in a line graph, then what pattern appears in the graph if there is an interaction? The lines move toward each other or cross. The lines in the graph are not straight (bent). The lines are separated by a space. The lines are parallel.

The lines move toward each other or cross.

To compute a two-sample independent-measures t-test, a researcher has to know several values. Which of the following is NOT a value that the researcher must know to compute this test? The sample mean for both samples The pooled sample variance The pooled population variance The sample size for both samples

The pooled population variance

In an independent-measures hypothesis test, what must be true if t = 0? The two sample variances must be equal. The two sample means must be equal. The two population means must be equal. The two sample means are not equal.

The two sample means must be equal.

What is stated by the null hypothesis for an ANOVA? There are no differences between any of the population means. All of the population means are different from each other. At least one of the population means is different from another mean. The beta estimate is significant.

There are no differences between any of the population means.

What is the purpose for post hoc tests? To determine whether or not a Type I error was committed To determine which treatments are significantly different To determine whether or not the sample is normally distributed To determine how much difference exists between the treatments

To determine which treatments are significantly different

For an independent-measures two-factor ANOVA, all of the F-ratios use the same value for the denominator of the ratio.

True

If a researcher expects that a new teaching technique will be more effective for children who are more than 10 years old than it is for younger children, then the researcher is predicting an interaction between the teaching technique and age.

True

Individual treatment conditions are also referred to as cells.

True

The individual conditions or values that make up a factor are called the levels of the factor.

True

The larger the differences among the sample means, the larger the numerator of the F-ratio will be.

True

Whenever a two-factor experiment results in a significant interaction, you should be cautious about interpreting the main effects because an interaction can distort, conceal, or exaggerate the main effects of the individual factors.

True

When comparing more than two treatment means, should you use an analysis of variance (ANOVA) rather than using several t-tests? If so, why? Yes. The analysis of variance is more likely to detect a treatment effect. No. There is no advantage to using an analysis of variance rather than several t tests. Yes. Using several t tests increases the risk of a Type II error. Yes. Using several t tests increases the risk of a Type I error.

Yes. Using several t tests increases the risk of a Type I error.

The results from a two-factor ANOVA show a significant main effect for Factor A and a significant main effect for Factor B. Based on this information, what can you conclude about the interaction between the two factors? The interaction cannot be significant. You cannot make any conclusions about the significance of the interaction. There probably is a significant interaction. There must be a significant interaction.

You cannot make any conclusions about the significance of the interaction.

In analysis of variance, each independent variable is referred to as a _____. stage factor level comparison

factor

A two-factor experimental design means that the researcher must measure two separate scores for each participant.

false

A two-factor independent-measures research study with 2 levels of Factor A and 2 levels of Factor B would require two separate groups of participants.

false

For a hypothesis test with the independent-measures t-statistic, the homogeneity of variances assumption states that the two sample variances are the same. (T/F)

false

For an analysis of variance comparing three treatment means, the null hypothesis states that all three population means are the same and the alternative hypothesis states that all three population means are different.

false

If other factors are held constant, the smaller the difference between two sample means is, the larger the value for the independent-measures t-statistic will be. (T/F)

false

If the A x B interaction is significant, then at least one of the two main effects must also be significant.

false

If the results of a two-factor ANOVA show no main effect for Factor A but show a significant interaction, then the results indicate that Factor A has no effect on the participants' scores.

false

In analysis of variance, MS total = MS between + MS within.

false

In general, a post hoc test enables you to go back through the data and compare the individual treatments two at a time, a process known as making pairwise comparisons.

true

One method for correcting the bias in the standard error is to "pool" the two sample variances using a procedure that allows the larger sample to carry more weight in determining the final value of the variance. (T/F)

true

The estimated standard error for the independent-measures t-statistic provides a measure of how much difference should exist, on average, between two sample means for samples selected from the same population. (T/F)

true

The independent-measures t-statistic uses the data from two separate samples to draw inferences about the mean difference between two populations or between two different treatment conditions. (T/F)

true

The within-treatments variance provides a measure of the variability inside each treatment condition.

true

Researchers conduct a hypothesis test and use data from two separate sets of observations drawn from the same group of participants. Their research design is called a repeated-measures design or a(n) _____ design. independent-measures within-subjects between-subjects dependent-measures

within-subjects

A researcher is investigating the study habits of first-year college students compared to senior students. The researcher collects data from 13 first-year students and 13 seniors and uses a two-tailed independent-measures t-test with α = .05. What is the appropriate critical value? ±2.056 ±2.064 ±1.711 ±1.706

±2.064

When conducted a two-sample independent-measures t-test, which of the following is the correct form of the null hypothesis statement? μ1 - μ2 = 0 μ1 - μ2 ≠ 0 μ1 = μ2 = 0 M1 - M2 ≠ 0

μ1 - μ2 = 0