Statistics - Hypothesis Testing Projects

Describe the similarities between an F-ratio and a T statistic. 6. A research study comparing three treatment

2. Describe the similarities between an F-ratio and a T statistic.

6. A research study comparing three treatment conditions produced means of M ₁ = 2, M ₂ = 4, M ₃ = 6.

Compute the variance for the set of three means. (Treat the means as a sample of n = 3 values and compute the sample variance)
Now we will change the third mean from M ₃ = 6 to M ₃ = 15. Notice that we have substantially increased the differences among the three means. Compute the variance for the new set of n=3 means. You should find that the variance is much larger than the value
obtained in part a. Note: The variance provides a measure of the size of the mean differences.

3. Using the data from the table below, respond to the following problem

An experimenter has investigated the effects of cigarette smoking on learning. Two levels of the smoking variable were used (smoked, did not smoke). There are also two levels of the learning variable (intentional learning and incidental learning).

(a) Practice the two-way between-subjects ANOVA on these data.

(b) Interpret the main effects and interaction of this experiment.

For an experiment comparing more than two treatment conditions you should use analysis of variance rather than separate t tests because __________.
A. you are less likely to make a mistake in the computations of ANOVA
B. a test based on variances is more sensitive than a test based on means
C. ANOVA has less risk of a Type I Error because several means are compared in one test
D. ANOVA has less risk of a Type II Error because several means are compared in one test
When the null hypothesis is true for an ANOVA, what is the expected value for the F-ratio?

0
B. 1.00
C. k - 1
D. N - k

3. An analysis of variance is used to evaluate the mean differences among three treatment conditions. The analysis produces SS _within = 20, SS _between = 40, and SS _total = 60. For this analysis, what is MS _between ?
A. 20/3
B. 20/2
C. 40/3
D. 40/2

4. In analysis of variance, the F-ratio is a ratio of
__________.
A. two (or more) sample means
B. two variances
C. sample means divided by sample variances
D. None of the other 3 choices is correct.

5. In an analysis of variance, large mean differences from one sample to another will pro-duce a large value for __________.
A. SSbetween treatments
B. SSwithin treatments
C. SStotal
D. Large mean differences will cause all three SS values to be large.

6. For an independent-measures experiment comparing two treatment conditions with a sample of n = 10 in each treatment, the F-ratio would have df equal to __________.
A. 18
B. 19
C. 1, 18
D. 1, 19

7. A researcher reports an F-ratio with df = 3, 36 for an independent-measures experiment. How many treatment conditions were compared in this experiment?
A. 3
B. 4
C. 36
D. 39

8. A treatment effect refers to differences between scores that are caused by the different treatment conditions. The differences (or variability) produced by treatment effects will contribute to __________.
A. the numerator of the F-ratio
B. the denominator of the F-ratio
C. both the numerator and the denominator of the F-ratio
D. Treatment effects do not contribute to the F-ratio because they are removed before the F-ratio is computed.

9. A research report concludes that there are significant differences among treatments, with "F(2,27) = 8.62, p < .01." How many treatment conditions were compared in this study?
A. 2
B. 3
C. 29
D. 30

10. The purpose of a post hoc test is to __________.
A. determine which treatments are different
determine how much difference there is between treatments
C. determine whether or not a Type I Error was made in the ANOVA
D. determine whether or not a complete ANOVA is justified

11. In general the distribution of F-ratios is __________.
A. symmetrical with a mean of zero
B. positively skewed with all values greater than or equal to zero
C. negatively skewed with all values greater than or equal to zero
D. symmetrical with a mean equal to df _between

12. A research study compares three treatments with n= 5 in each treatment. If the SS values for the three treatments are 25, 20, and 15, then the analysis of variance would produce SS _within equal to __________.
A. 12
B. 20
C. 60
D. cannot be determined from the information given

13. In the F-ratio for a repeated-measures ANOVA, variability due to individual differences __________.
A. is automatically eliminated from the numerator but must be computed and subtracted out of the denominator
B. is automatically eliminated from the denominator but must be computed and subtracted out of the numerator
C. is automatically eliminated from both the numerator and the denominator
D. must be computed and subtracted out of the numerator and the denominator

14. A repeated-measures study uses a sample of n = 8 participants to evaluate the mean differences among three treatment conditions. In the analysis of variance for this study, what is the value for df _total ?
A. 2
B. 7
C. 21
D. 23

15. A repeated-measures analysis of variance with a sample of n = 8 participants, produces df _within = 14. What is the value for df _error for this analysis?
A. 6
B. 7
C. 21
D. cannot determine without additional information

16. Which of the following are sources of variability that contribute to SS _between treatments in a repeated ANOVA?
A. treatment effect and chance/error
B. treatment effect and individual differences
C. treatment effect, individual differences, and chance/error
D. individual differences and chance/error

17. The results of a repeated-measures ANOVA are reported as follows, F(3, 27) = 1.12, p > .05. How many subjects participated in the study?
A. 40
B. 36
C. 10
D. 9

18. In Stage 1 of the repeated-measures ANOVA, total degrees of freedom is partitioned into
A. error df and between subjects df
B. within treatments df and between subjects df
C. between treatments df and between subjects df
D. between treatments df and within treatments df

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

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

21. The results of a two-factor analysis of variance produce df = 2, 24 for the F-ratio for factor A. Based on this information, how many levels of factor A were compared in the study?
A. 2
B. 3
C. 24
D. 25

22. The analysis of variance for a two-factor experiment produces __________.
A. one overall F-ratio followed by a series of required post hoc tests
B. two separate F-ratios
C. three separate F-ratios
D. four separate F-ratios

23. In a two-factor analysis of variance, the F-ratios for factor A, factor B, and the A x B interaction __________.
A. may have different df values but they all have the same denominator
B. all have the same df values and they all have the same denominator
C. may have different df values and may have different denominators
D. all have the same df values but they may have different denominators

24. If the results of a two-factor experiment are presented in a line graph, then an interaction can be seen whenever __________.
A. the lines in the graph are not straight (bent)
B. there is a space separating the lines
C. the lines are parallel
D. the lines move toward each other or cross

25. Refer to Exhibit 14-1. What value for the missing mean would result in no interaction (SSA x B = 0)?

Exhibit 14-1- Treatment means.

B1
B2

A1
M = 6
M = 8

A2
M = 12
M = ?

A. 2
B. 10
C. 12
D. 14

26. A negative value for a correlation indicates __________.
A. a much stronger relationship than if the correlation were positive
B. a much weaker relationship than if the correlation were positive
C. increases in X tend to be accompanied by increases in Y
D. increases in X tend to be accompanied by decreases in Y

27. A Pearson correlation of r = -0.85 indicates that a graph of the data would show __________.
A. points clustered close to a line that slopes up to the right
B. points clustered close to a line that slopes down to the right
C. points widely scattered around a line that slopes up to the right
D. points widely scattered around a line that slopes down to the right

28. A set of n = 5 pairs of X and Y values has SX = 10, SY = 20, and SXY = 60. For this set of scores, the value of SP is __________.
A. -20
B. -28
C. 20
D. 60

31. Suppose the correlation between height and weight for adults is +0.80. What proportion (or percent) of the variability in weight can be explained by the
relationship with height?

80%
B. 64%
C. 100 - 80 = 20%
D. 40%

32. For a sample of n = 20 individuals, how large a Pearson correlation is necessary to be statistically significant for a two-tailed test with a = .05?
A. 0.444
B. 0.433
C. 0.423
D. 0.413

33. Under what circumstances should the Spearman correlation be used?
A. The researcher's primary interest is the linearity of the relationship.
B. The original data are measured on an ordinal scale of measurement.
C. The Pearson is too difficult to compute.
D. All of the other options are appropriate circumstances for the Spearman correlation.

34. In what situations can the point-biserial correlation be used?
A. When an independent-measures t test would also be appropriate.
B. When both X and Y are ranks.
C. When a single-sample t test would also be appropriate.
D. When both X and Y are dichotomous.

35. In the general linear equation, Y = bX + a, what is the value of b called?
A. X intercept
B. Y intercept
C. correlation between X and Y
D. slope

36. The regression equation is determined by minimizing __________.
A. the total error between the X and Y values
B. the total error between the predicted Y values and the actual Y values
C. the total squared error between the X and the Y values
D. the total squared error between the predicted Y values and the actual Y values

37. Which of the following points is on the line defined by the equation, Y = 4X + 2?
A. X = 0 and Y = 2
B. X = 1 and Y = 4
C. X = 2 and Y = 8
D. X = 3 and Y = 9

38. If there is a negative correlation between X and Y then the regression equation, Y = bX + a will have __________.
A. b > 0
B. b < 0

D. a < 0

39. The term observed frequency refers to __________.
A. the frequencies found in the sample data
B. the frequencies found in the population being examined
C. the frequencies computed from the null hypothesis
D. the frequencies that are hypothesized for the population being examined

40. The expected frequencies __________.
A. are always whole numbers
B. can contain fractions or decimal values
C. can contain both positive and negative values
D. can contain fractions and negative numbers

41. The chi-square distribution is __________.
A. symmetrical with a mean of zero
B. positively skewed with all values greater than or equal to zero
C. negatively skewed with all values greater than or equal to zero
D. symmetrical with a mean equal to n - 1

42. A researcher is using a chi-square test to determine whether there are any preferences among four brands of cola. With a = .05 and a sample of n = 30, what is the boundary for the critical region for the hypothesis test?
A. 7.81
B. 9.49
C. 42.56
D. 43.77

43. A chi-square test for goodness of fit is used to test whether or not there are any preferences among three brands of cola. If the study uses a sample of n = 60 subjects, then the expected frequency for each category would be __________.
A. 1
B. 15
C. 20
D. 30

44. What does it mean to obtain a negative value for the chi-square statistic?
A. The observed frequencies tend to be larger than the expected frequencies.
B. The expected frequencies tend to be larger than the observed frequencies.
C. There are large discrepancies between the observed and expected frequencies for most categories.
D. The chi-square statistic can never be negative.

45. The chi-square test for goodness of fit evaluates __________.
A. the relationship between two variables
B. the mean differences between two or more treatments
C. the shape or proportions for a population distribution
D. None of the other options are evaluated by the chi-square test.

46. The null hypothesis for the chi-square test for independence states that __________.
A. there is a relationship between the two variables
B. there is no relationship between the two variables
C. both variables have the same frequency distribution
D. the two variables have different frequency distributions

47. A chi-square test for independence has df = 2. What is the total number of categories (cells in the matrix) that were used to classify individuals in the sample?
A. 2
B. 3
C. 4
D. 6

48. The chi-square statistic should not be used if __________.
A. fe > 5 for any cell
B. fe < 5 for any cell
C. fe = fo for any cell
D. None of the other options is correct.

49. A sample of 100 people is classified by gender (male/female) and by whether or not they are registered voters. The sample consists of 80 females and 20 males, and has a total of 60 registered voters. If these data were used for a chi-square test for independence, the expected frequencies should have __________ males who are registered voters.
A. 12
B. 20
C. 40
D. cannot determine without additional information

50. Under what conditions can the phi-coefficient be used to measure effect size for a chi-square test for independence?
A. When both variables consist of exactly two categories
B. When both variables consist of more than two categories
C. When either of the two variables consists of exactly two categories
D. When either of the two variables consists of more than two categories