Stats Exam 3
On average, what value is expected for the F-ratio if the null hypothesis is true
1.00* N-k 0 k-1
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 6 3 9*
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?
12* 3 4 7
A researcher reports t(22) = 5.30, p < .01 for an independent-measures study. How many individuals participated in the study?
24* 21 22 23
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?
25 30* 5 10
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 3.74 3.34 3.88*
Which set of sample characteristics is most likely to produce a significant value for the independent-measures t-statistic?
A small mean difference and large sample variances A small mean difference and small sample variances A large mean difference and large sample variances A large mean difference and small sample variances*
In an analysis of variance, what is a factor?
A treatment total A dependent variable An independent (or quasi-independent) variable* A treatment mean
What is stated by the alternative hypothesis for an ANOVA
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. All of the population means are different from each other.
Which of the following is an assumption for computing any type of independent-measures t-tes
Data in the population being sampled are normally distributed. Data were obtained from a sample that was selected using a random sampling procedure. The probabilities of each measured outcome in a study are independent. All of the above*
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.
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?
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.*
Which of the following is an assumption for the two-sample independent-measures t-test, but not the one-sample t-test?
Equal variances* Independence Random sampling Normality
For an independent-measures t-statistic, what is the effect of increasing the number of scores in the sample?
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.* 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.
In general, what factors are most likely to reject the null hypothesis for an ANO
Large mean differences and small variances* Small mean differences and small variances Small mean differences and large variances Large mean differences and large 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 within* SS between should be about the same size as SS within SS between should be about the same size as SS total MS between should be about the same size as MS total
What provides a measure of the variance caused by random, unsystematic differences?
SS Total df Within The F ratio The error term*
In analysis of variance, which value is determined by the size of the sample mean differences?
SS within df between df within SS between*
Which of the following describes a typical distribution of F-ratios?
Symmetrical with a mean of zero Positively skewed with all values greater than or equal to zero* Negatively skewed with all values greater than or equal to zero Symmetrical with a mean equal to df Total
What is stated by the null hypothesis for an ANOVA?
The beta estimate is significant. All of the population means are different from each other. There are no differences between any of the population means.* At least one of the population means is different from another mean.
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 population means are equal to each other. The difference between the two population means is not equal to 0.* The difference between the two sample means is equal to 0.
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. There must be a significant interaction. You cannot make any conclusions about the significance of the interaction.* There probably is a significant interaction.
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 are parallel. The lines are separated by a space. The lines in the graph are not straight (bent).
A one-way ANOVA makes several assumptions. Which of the following is NOT one such assumption?
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)* The observations within each sample must be independent. The populations from which the samples are selected must be normal.
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 population variance* The pooled sample variance The sample size for both samples
In a two-factor ANOVA, what is the implication of a significant A x B interaction?
The significance of the interaction has no implications for the main effects.* Both of the main effects must also be significant. Neither of the two main effects can be significant. At least one of the main effects must also be significant.
In analysis of variance, what is measured by the MS values?
The total variability for the set of N scores Population variances Sample variances* The average distance from one mean to another
In an independent-measures hypothesis test, what must be true if t = 0?
The two population means must be equal. The two sample variances must be equal. The two sample means must be equal.* The two sample means are not equal.
What is the purpose for post hoc tests?
To determine which treatments are significantly different* To determine whether or not a Type I error was committed To determine whether or not the sample is normally distributed To determine how much difference exists between the treatments
A two-factor ANOVA with 2 levels of Factor A and 3 levels of Factor B involves 6 separate hypothesis tests.
True False*
A two-factor experimental design means that the researcher must measure two separate scores for each participant.
True 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.
True 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.
True False*
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.
True 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.
True 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.
True False*
If the A x B interaction is significant, then at least one of the two main effects must also be significant.
True 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.
True False*
In analysis of variance, MS total = MS between + MS within.
True False*
Obtaining a significant interaction means that both Factor A and Factor B have significant main effects.
True False*
The null hypothesis for the independent-measures t-test states that there is no difference between the two sample means.
True False*
Two separate samples, each with n = 10 scores, will produce an independent-measures t-statistic with df = 19.
True False*
When pooling variances, the resulting value will be closer to the variance for the sample with the smaller number of scores.
True False*
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* False
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* False
F-ratios are always greater than or equal to 0.
True* False
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* False
For a hypothesis test with the independent-measures t-statistic, the null hypothesis states that the two population means are the same.
True* False
For a two-factor ANOVA, the significance of any specific F-ratio is completely independent of the significance of the other F-ratios.
True* False
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.
True* False
For an independent-measures two-factor ANOVA, all of the F-ratios use the same value for the denominator of the ratio.
True* False
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* False
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* 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* False
Individual treatment conditions are also referred to as cells.
True* False
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.
True* False
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.
True* False
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.
True* False
The individual conditions or values that make up a factor are called the levels of the factor.
True* False
The larger the differences among the sample means, the larger the numerator of the F-ratio will be.
True* False
The within-treatments variance provides a measure of the variability inside each treatment condition.
True* False
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* False
How many separate F-ratios are used in a two-factor ANOVA
Two overall F-ratios One overall F-ratio Three overall F-ratios* Four overall F-ratios
Which of the following is best to present a structure of a two-factor experiment?
Venn diagram Pie chart Matrix* Bar chart
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. Using several t tests increases the risk of a Type I error.* 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.
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.
between-subjects dependent-measures within-subjects* independent-measures
A research design that uses a separate group of participants for each treatment condition is called an independent-measures design or a _____ design.
dependent-measures repeated-measures within-subjects between-subjects*
In analysis of variance, each independent variable is referred to as a ____
factor* level stage comparison
In a two-factor analysis of variance, a main effect is defined as the
mean difference between the two factors. mean differences among the levels of one factor.* difference between the largest treatment mean and the smallest treatment mean. mean differences among all treatment conditions.
Computing an independent-samples t-test is appropriate when
participants are observed and measured only once. different participants are assigned to each group. the population variance is unknown. All of the above*
A key difference between a t statistic and a z statistic is that the standard error is _____ to compute a t statistic.
placed in the numerator replaced removed estimated*
Two variables are said to interact when
the effect of one independent variable depends on the levels of the second variable.* both variables produce a change in the participants' scores. both variables are equally influenced by a third factor. the two variables are differentially influenced by a third variable.
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 ±1.711 ±2.064* ±1.706
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 M1 - M2 ≠ 0 μ1 = μ2 = 0
The percentage of variance accounted for by the treatment effect is usually known as _____ in published reports of ANOVA results.
σ² μ² α² η²*