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Page 1 True / False Questions 1) ___ The independent-samples t-test cannot be used when samples differ in size. 2) ___ Assuming the null hypothesis (H0: µ1= µ2), the single most frequently occurring value in the sampling distribution of mean difference is 0. 3) ___ If you compute a negative value of the independent-samples t statistic, you know you’ve made a mistake. 4) ___ If your computed value of the independent-samples t statistic is 0, you know you’ve made a mistake. 5) ___ In the context of the independentsamples t-test, the alternative hypothesis says the obtained X 1 – X 2 difference is probably a result of the samples having come from different populations. 6) ___ In the context of the independentsamples t-test, a statistically significant difference tells us that the obtained X 1 – X 2 difference would probably not be the result of sampling error alone. 7) ___ Sampling error alone cannot cause two sample means to differ. 8) ___ All other things being equal, the further the t statistic falls from 0, either in the positive or negative direction, the more likely it is that the difference is significant. 11) ___ The two-tail independent-samples t-test is more powerful than the one-tail test. 12) ___ With a nondirectional hypothesis, a value of t = -4.7 is more likely to be statistically significant than is a value of t = +1.5, assuming a constant sample size. 13) ___ We could use a dependent-samples t-test to compare mean levels of achievement motivation before and after exposure to a motivation workshop. 14) ___ If you compute a negative value for the F ratio, you know you’ve made a mistake. 15) ___ If two samples that were treated identically show a difference that is statistically significant, it is a Type II error. 16) ___ If two samples are drawn from very different populations and yet are so similar that they are not identified as statistically significant, it is a Type II error. 17) ___ A Type I error involves concluding that two samples came from the same population when they actually came from different populations. 18) ___ We can reduce the probability of making a Type II error by increasing sample sizes. 19) ___ The one-way ANOVA can only have one factor. 9) ___ A X 1– X 2 difference that produces a large value of t is located toward the center of the sampling distribution of the difference. 20) ___ One-way ANOVA assumes that the populations represented by the samples at hand have approximately equal variances. 10) ___ We use a one-tail independentsamples t-test when we have not predicted the direction of the difference in advance of collecting data. 21) ___ The one-way ANOVA becomes more robust to violations of its assumptions if samples sizes are large and equal. Page 2 22) ___ In a series of 100 t-tests, each at the .05 level of significance, you would expect 5 tests to produce false significance as a result of Type I errors. 23) ___ No matter how many groups are being compared, the omnibus F test from the one-way ANOVA uses only one significance test. 24) ___ A significant F test from a one-way ANOVA tells us that there is a significant difference somewhere among the means, but doesn’t tell us where it is. 25) ___ Post hoc comparison procedures are performed prior to doing one-way ANOVA in order to identify likely sources of significance. 26) ___ Within-group variance is caused by sampling error and treatment effects. 27) ___ The stronger the treatment effect, the greater the within-group variance. 28) ___ Between-group variance is affected by treatment effects. 29) ___ Between-group variance is affected by individual difference characteristics. 30) ___ Between-group variance is affected by measurement error. 31) ___ Individual difference characteristics from one case to the next do not affect within-group variance. 32) ___ The F statistic compares the ratio of between-group variance to withingroup variance. 33) ___ If you compute a value of F = 0, you know you’ve made a mistake. 34) ___ If you compute a value of F = -1.5, you know you’ve made a mistake. 35) ___ In the sampling distribution of F, small values are fairly common and larger values are less common. 36) ___ All other things being equal, as differences among group means increase, SSBetween increases. 37) ___ In the context of one-way ANOVA, when we declare a difference nonsignificant, it means that we have rejected the null hypothesis. 38) ___ If the F from one-way ANOVA is significant but none of the pairwise differences meets or exceeds Tukey’s HSD, we must conclude that the significant F was a Type I error. 39) ___ The statistic eta-square (η2) can be used to measure the strength of the association between the independent and dependent variables in a one-way ANOVA. 40) ___ In the context of one-way ANOVA, eta-square can range in value from –1 to 0 to +1. 41) ___ In the parlance of ANOVA, a “factor” is the same thing as a dependent variable. 42) ___ Independent variables in the factorial can be measured at the nominal scale of measurement. 43) ___ One-way ANOVAs tell us about main effects, but do not address interaction effects. 44) ___ A main effect refers to the effect of one independent variable without regard to any other independent variables. 45) ___ When there is an interaction effect, the effect of one independent variable is different depending on the level of some other independent variable. Page 3 46) ___ A three-way ANOVA includes three independent variables and one dependent variable. 57) ___ MSA measures variance due to individual differences, measurement error, and the Factor A main effect. 47) ___ A study of the effects of gender (male vs. female) and educational level (less than high school, high school, some college, college graduate or above) on income would be an example of a 2 x 4 factorial ANOVA. 58) ___ MSAB measures variance due to individual differences, measurement error, Factor A, Factor B, and the A x B interaction effect. 48) ___ In a fully crossed factorial design, the number of different treatment combinations is found by multiplying together the number of levels of each independent variable. 49) ___ All of the factors in a completely randomized factorial ANOVA are “within-subjects” factors. 59) ___ MSWithin measures variance due to individual differences and measurement error. 60) ___ Main effects are generally viewed as more important than interaction effects in the factorial ANOVA. Multiple Choice and Short Answer 50) ___ In completely randomized factorial ANOVA, each cell of the data table is represented by a different group of cases. Items 61-62 refer to the following sample data from two randomly selected samples from normally distributed population: Sample 1: Mean = 40, s = 8, n=11. Sample 2: Mean =34, s=10, n=21. 51) ___ An interaction effect is indicated by a line graph in which the lines are nonparallel. 61) What are the degrees of freedom associated with the t-test? ___________ 52) ___ A split-plot factorial ANOVA includes one or more within-subjects factors and one or more between-subjects factors. 62) The “pooled” estimate of the error variance is ____. a) 64 b) 88 c) 100 d) 164 53) ___ In a factorial ANOVA one can either see main effects or interaction effects, but not both. 54) ___ A disordinal interaction effect is indicated in a line graph by lines that diverge, but do not actually cross. 55) ___ A ordinal interaction effect is indicated in a line graph by lines that cross. 56) ___ The F tests in factorial ANOVA compare different variances in order to determine if differences among means are significant. 63) If the t-test was conducted using no correction to the df for unequal variance (i.e., assuming the variances were equal), this situation _____. a) would not affect Type I error rate. b) is “conservative” thus makin a Type II error more likely c) is “liberal” thus making a Type I error more likely. Page 4 64) A researcher set _ = .05, and carried out 20 independent t-tests. By chance alone, how many statistically significant t-tests would be expected if Ho is true in each of the 20 situations? ________ 65) Which of the following does not belong with the others? a) An observed t-ratio is less than the critical t-ratio. b) The null hypothesis is rejected. c) The null hypothesis is tenable. d) The difference in sample means results from sampling error e) The statistical evidence is insufficient to rule out chance as a credible explanation of the data. 66) Whether a one-tailed or a two-tailed test is called for depends upon the a) size of the samples b) shapes of the distributions from which the samples are drawn. c) tenability of the underlying assumptions for the tests. d) nature of the reserach hypothesis. e) observed difference in the two sample means. 67) The critical t-ratio required for statistical significance is smaller (in absolute value) when using a) a directional rather than a nondirectional test. b) a non-directional rather than a directional test. c) samples with fewer degrees of freedom. d) a two-tailed test rather than a onetailed test 68) Which of the following is least like the other three? a) Matched observations b) Correlated observations c) Related samples d) Paired scores e) Independent observations 69) The probability of a type-II error in t-tests of means is reduced by a) relaxing α (e.g., from .01 to .05) b) increasing the samples sizes. c) making a treatment more effective, hence increasing the difference in population means. d) All of the above e) None of the above 70) The one-factor analysis of variance is used primarily to test statistical hypotheses concerning a) variances b) means c) mean squares d) standard deviations 71) If n1 = 19, n2 =21, and n3 = 23, the within groups degrees if freedom for a one-factor ANOVA would EQUAL ________. 72) In a one-factor ANOVA, a rejection of the null hypothesis implies that a) the J population means are equal. b) the J population variances are not equal c) each mean differs significantly from the other J-1 means. d) each variance differs significantly from the other J-1 variances. e) some subset of population means differs from some other subset of population means. 73) In a one-factor ANOVA with the independent variable is comprised of two levels. If SSb = 20 and Msw = 4, the F-ratio for testing the null hypothesis would equal ___. a) 1 b) 2 c) 5 d) 10 e) 40 Page 5 Items 74-76 are based on the following information: For a one-factor ANOVA with J =2 treatment groups, the within-groups sum of squares is 100, the sample mean of group I is 5, the sample mean of group II is 7, and the sample size of both groups is n=6. 74) The numerical value of Msw is ______. 75) The numerical value of Msb is 80) The F -ratio of 4.5 is a) significant with α = .05. b) tenable with α = .05. c) significant with α = .10 and .05. 81) It is an assumption in the one-way ANOVA that a) the sample variances are the same for the J groups. b) the population variances are the same for the J groups. c) the group(s) with the larger variances also have larger n’s ________. 76) Estimate the numerical value of the standard deviation of the raw scores in a group from its group mean assuming homogeneity of variance. a) 6 b) 10 c) 3.16 d) 100 77) Suppose a one-factor ANOVA with J = 2 yielded an F-ratio of 4.00. The analysis of the same data using the t-test for independent samples would a) result in an inflated type-I error rate. b) yield a t-ratio of 2. c) yield a t-ratio of 4. d) be less apt to reject Ho. Items 78-80 are based on the following ANOVA summary table: SV df MS F -------------------------------------------Between 2 45 4.5 Within 78 10 78) How many groups are being compared in this analysis? ________ 79) The total number of subjects in this study was ________. 82) Given a one-factor ANOVA in which the null hypothesis is false: If the number of observations per group (n) is increased, the probability of rejecting Ho (assume that all other factors remain constant) is a) increased b) remains constant c) decreased 83) How many different pair-wise t-tests would be possible from a set of six means? a) 5 b) 6 c) 15 d) 30 e) None of these 84) When a one-factor ANOVA results in a significant F-ratio for J=2, one should follow the ANOVA with the a) Tukey MC b) HSD technique c) LSD technique. d) t-test e) None of these are necessary 85) If a family error rate for α is desired, and hypotheses involving all pairs of means are to be tested, one should select the ___ method of multiple comparisons (MC). a) Dunnett b) Tukey c) Scheffe d) LSD Page 6 86) Given Ho is true and using the .05 level of significance, if a t-test is used to compare the largest mean with the smallest mean in a set of 6 means, the probability of a typeI error is___. a) equal to .05 b) >.05 c) <.05 87) In one investigation, it was found that children age 12 learn better when allowed to discover rules whereas children age 6 learn better when taught didactically. This is an example of a) regression b) interaction c) a type-I error d) a type-II error e) a double main effect Items 88-89: Consider a two-factor design with 5 rows, 3 columns, and 2 persons per cell. 88) The number of degrees of freedom associated with Msw is _______. 89) The number of degrees of freedom for the interaction is _______. 90) In ANOVA, interaction of two variables is certainly present when a) the two variables are positively correlated b) the two variables are negatively correlated c) the row effects are not consistent across columns d) the main effects do not account for all of the observed variance among the observations. e) the main effects and the within-cell variance account for all of the observed variation. Items 91-95 are based on the following ANOVA summary table (α = .01): Source df MS F ____________________________________ Anxiety treatment (A) 2 45 4.5 Ability levels (B) 1 70 7.0 AxB 2 170 17.0 Within 60 10 91) For which source of variation is the null hypothesis rejected at the .01 level of significance? a) Anxiety (A) b) Ability (B) c) A x B d) All of the above 92) How many cells were there in the above design? ________ 93) The total sample size (n..) for the ANOVA summary table above is ________. 94) In the ANOVA summary table above, SSAxB would equal a) 170 b) 340 c) 510 d) 1020 95) Estimate the numerical value of the standard deviation of the raw scores within a cell. a) 3.16 b) 10 c) 100 d) 780 Page 7 96) In the context of the independent-samples t-test, the alternative hypothesis states that a) the two samples probably came from different populations b) the two samples probably came from the same population c) the difference between the two samples is probably due to rounding error d) the difference between the two samples is probably due to sampling error 97) In the context of the independent-samples t-test, the null hypothesis states that _____. a) the two samples differ significantly b) the two samples do not differ in mean value c) the difference is unlikely due to sampling error d) the difference is unlikely due to rounding error 98) Under the null hypothesis, the single most likely value in the sampling distribution of the mean difference is _____. a) 0 b) 1 c) N1 + N2 – 2 99) What has occurred when two samples, drawn from two different populations, are found NOT to differ significantly? a) we have accepted the alternative hypothesis b) Type I error c) we have accepted the null hypothesis d) Type II error 100) In a study involving J = 7 samples, how many pairwise comparisons are possible? ________ 101) In a series of 1000 one-way ANOVAs, each using the .01 level of significance, how many would you expect to produce Type I errors? ________ 102) The variability seen within each group in a one-way ANOVA is due to: a) sampling error b) treatment effects c) measurement error and treatment effects d) measurement error and individual differences 103) Which of the following does NOT affect within-group variance? a) treatment effects b) measurement error c) individual differences d) treatment error 104) Which of the following cause(s) between-group variance? a) treatment effects b) measurement error c) individual differences d) all of the above 105) What result would you expect if data were collected under better controlled, more rigorous conditions? a) within-group variance would probably increase b) within-group variance would probably decrease c) between-group variance would probably increase d) the value of F would probably decrease 106) When between-group variance is larger than within-group variance, it is because of _____. a) measurement error b) individual differences c) treatment effects d) none of the above Page 8 107) What happens to the value of F as the sample means become more widely separated? a) it increases b) it decreases c) nothing happens to F d) none of the above 108) If the sample means were identical, you would expect to see _____. a) SSBetween = 1 b) SSWithin = 0 c) MSBetween = 0 d) MSWithin = 1 109) Ten males and 10 females have each been exposed first to 10, then 20, and finally 50 mg of an experimental antidepressant drug. Which factorial ANOVA would be used in analyzing these data? a) randomized factorial ANOVA b) one-way block ANOVA c) split-plot factorial ANOVA 110) If levels of Factor A are plotted on the abscissa and levels of Factor B are plotted as separate lines in a line graph, what pattern would suggest a main effect of Factor B? a) parallel lines that are widely separated b) parallel lines that are close together c) lines that cross at the middle, forming a perfect X d) none of the above 111) If levels of Factor A are plotted on the abscissa and levels of Factor B are plotted as separate lines in a line graph, what pattern would suggest a main effect of Factor A? a) parallel lines that are widely separated b) parallel lines that are both slanted sharply upward from left to right c) parallel lines that are close together and perfectly horizontal d) none of the above 112) An interaction effect is depicted in a line graph by _____. a) parallel lines that are widely separated and slant sharply b) lines that are nonparallel, but do not cross c) parallel lines that are perfectly horizontal 113) In factorial ANOVA, the size of SSWithin is affected by _____. a) measurement error b) measurement error and individual differences c) measurement error, individual differences, and sample size d) measurement error, individual differences, sample size, and treatment effects 114) In factorial ANOVA, which of the following influences MSBetween? a) Factor A treatment effect b) Factor B treatment effect c) A x B interaction effect d) all of the above 115) In a 4 x 5 factorial ANOVA, how many omnibus F tests are there? ____________ 116) In a 3 x 5 factorial ANOVA, how many interaction effects are there? ____________ 117) In a 2 x 4 x 3 factorial ANOVA, how many omnibus F tests are there? ____________ 118) In a 2 x 2 factorial design, how many post hoc pairwise comparisons are necessary to identify the source(s) of significant main effects of Factors A and B? a) 0 b) 1 c) 2 d) 6 Page 9 119. In a one factor ANOVA with J = 4 groups and nj = 5 subjects per group: X 1 = 22, X 2 = 24, X 3 = 20, X 4 = 26 What are the Between-Group Sum of Squares? 120. Determine the F-ratio which results from the given one-way ANOVA data. Source df SS MS F _____________________________________ Betweeen 4 30.5 Within _____________________________________ Total 99 165.0 121. For the data in question 2, the estimated percent variance in the dependent variable accounted for (i.e., η2) by the independent variable is: 122. Assuming equal sample sizes, how many subjects (nj) were in each of the groups. question 2. 123. A one-factor ANOVA is performed on five groups with: n1 = 10, n2 = 6, n3 = 12, n4 = 15, and n5 = 20 scores in the groups. Given B = Between and W = Within; in the analysis of these data, what are the degrees of freedom (df) for A. Between-Group Factor? ______ B. Within or Error? ______ 124. Assume a (A = 3) X (B = 4) two factor ANOVA with njk = 8 scores per cell. What are the degrees of freedom (df) for the A. A main effect? ______ B. B main effect? ______ C. AxB interaction? ______ D. Within or Error? ______ 125-127. The following two-factor ANOVA results were obtained after analyzing the dependent variable scores of participating subjects. Source df MS F _____________________________________ A 2 55 5.50 B 1 60 6.00 AxB 2 130 13.00 Within 80 10 125. How many subjects participated in the study? 126. What is the estimated percent variance in the dependent variable accounted for (i.e., η2) by A. A main effect? ______ B. B main effect? ______ C. AxB interaction? ______ 2 Note: You may compute η or partial η2. 127. Assuming equal sample sizes, how many subjects were in each of the groups? Page 10 128-133. Below are cell means based on a factorial design with nj = 25 subjects per cell. Assume that the within cell variance of the scores is quite small. If a two-factor ANOVA were performed, which of the following statements would most probably be true? Use one of the following options to answer to the next 6 questions (68-73). a. Only the row (A) main effect is significant b. Only the column (B) main effect is significant c. Only the interaction (AB) effect is significant d. The row main (A) effect and the column main (B) effect are significant, but there is no interaction (AB) effect. e. The row main (A) effect and the interaction (AB) effect are both significant f. The column main (B) effect and the interaction (AB) effect are both significant Hint: Marginal means and Graphing may be helpful. 128. ____ A1 A2 A3 I I I I B1 35 60 85 B2 85 60 35 129. ___ A1 A2 A3 I I I I B1 15 40 15 B2 65 40 35 130. ____ A1 A2 A3 I I I I B1 15 10 25 B2 65 60 75 131. ____ A1 A2 A3 I I I I B1 15 15 15 B2 35 35 35 132. ____ A1 A2 A3 I I I I B1 35 15 55 B2 55 25 25 133. ____ A1 A2 A3 I I I I B1 25 15 35 B2 45 55 35 134. The following split-plot ANOVA results were obtained after analyzing the dependent variable scores of participating subjects. B = Between-Subjects Factor RM = a Repeated Measures Factor, S(B) Subjects nested within the Between-Subjects Factor. Source B RM B x RM S(B) RM X S(B) TOTAL df 2 3 6 27 81 MS 45 70 170 10 8 119 F 4.50 8.75 21.25 A. How many subjects participated in the study? B. Assuming the Between-Subjects Grouping factor had equal samples sizes, how many subjects per group were there? C. How many times were they measured? Page 11 The following four questions (135-138) are based on the four graphic options below. Each graph depicts the interaction of treatment (T vs. C) with prior ability (L, M, H). T T C A. L M C H B. T T C C. L M H C D. L M _____ 135. Fability is significant with L < M ≈ H; Ftreatment is significant with T > C; and Finteraction is significant. _____ 136. A disordinal interaction (Finteraction is significant); Fability is not significant; Ftreatment is not significant _____ 137. An ordinal interaction (Finteraction is significant); Fability is not significant; Ftreatment with T > C is significant _____ 138. Fability is significant with L < M < H; Ftreatment is significant with T > C; and Finteraction is not significant. H