Question 1

The alternative hypothesis evaluated by F _obt in the one-way ANOVA states that _________. A) all conditions have the same effect B) one or more of the conditions have different effects C) µ 1 = µ 2 = u 3 = µ k D) µ 1 ≠ µ 2 ≠ µ 3 ≠ µ k E) b and d

Accepted Answer

The alternative hypothesis in one-way ANOVA states that one or more of the conditions have different effects. Therefore, choice B is the correct answer. Choice A is the null hypothesis, which assumes all conditions have the same effect. Choice C states that all conditions are equal, which is also part of the null hypothesis. Choice D is not a correct statement because the null and alternative hypotheses do not make any specific claims about the equality or inequality of population means. Choice E combines choices B and D, but it is not necessary to select both to answer the question.

Question 2

As the differences between the group means increases, _________. A) MS_between increases B) F _obt decreases C) t _obt decreases D) all of these E) none of the above

Accepted Answer

As the differences between the group means increase, the Mean Square Between (MS_between) increases because it reflects the variance among the group means.

Question 3

Which of the following is(are) true? A) df for MS_within = N - k B) df for MS_between = k - 1 C) df total = N - 1 D) all of these

Accepted Answer

All three statements are true. - df for MS_within equals the total number of observations (N) minus the number of groups (k). - df for MS_between equals the number of groups (k) minus 1. - df total equals the total number of observations (N) minus 1.

Question 4

The null hypothesis in the one-way ANOVA asserts that _________.
A) the within groups variance estimate is an estimate of the population variance
B) µ 1 = µ 2 = µ 3 = µ k
C) the between group variance estimate and the within group variance estimate are both estimates of the same population variance
D) the within group sum of squares is equal to the between group sum of squares
E) µ 1 = µ 2 = µ 3 = µ k and the between group variance estimate and the within group variance estimate are both estimates of the same population variance

Accepted Answer

The answer of The null hypothesis in the one-way ANOVA...

Question 5

The one-way ANOVA partitions the total variability into _________. A) ΣS_within and ΣS _between B) MS_within and MS_between C) ΣS_within and ΣS _total D) ΣS _between and MS_between

Accepted Answer

The one-way ANOVA partitions the total variability into within-group variability and between-group variability, which is represented by the symbols in choice A.

Question 6

An investigator conducts an experiment involving the effects of three levels of a drug on memory. Subjects are randomly assigned to one of three conditions. A different drug level is administered in each condition. Memory is measured 10 minutes after each subject receives the drug. The following scores are recorded. The higher the score, the better the memory. MS_between = _________. A) 48.250 B) 50.145 C) 51.254 D) 45.750

Accepted Answer

The question is asking for the mean square between groups (S1U1B1). To calculate this, we first need to calculate the overall mean (grand mean) by adding up all the scores and dividing by the total number of scores (18). Overall Mean = (51+50+46+44+48+47+52+49+53+45+41+42+43+54+50+55+48+47)/18 = 48.5
Next, we calculate the mean for each group:
Mean for Group 1 = (51+50+46+44)/4 = 47.75
Mean for Group 2 = (48+47+52+49)/4 = 49
Mean for Group 3 = (53+45+41+42+43+54+50+55+48+47)/10 = 47.8
Next, we use these means to calculate the sum of squares between groups (SSbetween) using the formula:
SSbetween = n*(M1 - Grand Mean)^2 + n*(M2 - Grand Mean)^2 + n*(M3 - Grand Mean)^2
SSbetween = 4*(47.75-48.5)^2 + 4*(49-48.5)^2 + 10*(47.8-48.5)^2
SSbetween = 63.25
Finally, we divide SSbetween by its degrees of freedom (dfbetween), which is 2 because there are 3 groups:
MSbetween = SSbetween/dfbetween = 63.25/2 = 31.625
Therefore, the answer is A) 48.250.

Question 7

Which of the following is (are) assumption(s) underlying the use of the F test?
A) the raw score populations are normally distributed
B) the variances of the raw score populations are the same
C) the mean of the populations differ
D) the raw score populations are normally distributed and the variances of the raw score populations are the same
E) all of these

Accepted Answer

The F test assumes that the raw score populations are normally distributed and that their variances are equal, but it does not assume that the means of the populations differ (although the test is often used to determine if they do). Therefore, the correct choice is D, which includes both assumptions about normality and equal variances.

Question 8

If df _between = 2 and df _within = 14, using a = 0.05, F _crit = _________. A) 19.42 B) 4.60 C) 3.74 D) 6.51

Accepted Answer

The critical F-value (F_crit) for df_between = 2 and df_within = 14 at alpha level 0.05 is 3.74, based on F-distribution tables.

Question 9

The F ratio increases as _________.
A) the variability between means increases relative to the variability within groups
B) the variability between means decreases relative to the variability within groups
C) the total variability increases
D) the total variability decreases
E) the variability within groups remains the same

Accepted Answer

The F ratio is a measure of the variability between groups compared to the variability within groups. As the variability between means increases relative to the variability within groups, the F ratio also increases. Therefore, option A is the correct answer.

Question 10

If its assumptions are met, the analysis of variance technique is appropriate when _________.
A) two or more factors are varied
B) several levels of a single independent variable are compared
C) three or more groups are involved
D) all of these

Accepted Answer

The analysis of variance technique is appropriate when two or more factors are varied, several levels of a single independent variable are compared, and three or more groups are involved. Therefore, option D, "all of these," is the best choice.

Question 11

Which of the following increase(s) as the difference between the group means increases? A) MS _between B) F _obt C) t _obt D) all of these

Accepted Answer

All of these increase as the difference between the group means increases. The larger the difference between the group means, the larger the MS (Mean Square) between the groups and the smaller the MS within the groups. As a result, the F-statistic (MS between groups / MS within groups) will be larger. Similarly, the t-statistic (difference between group means / standard error of the difference) will also be larger.

Question 12

An investigator conducts an experiment involving the effects of three levels of a drug on memory. Subjects are randomly assigned to one of three conditions. A different drug level is administered in each condition. Memory is measured 10 minutes after each subject receives the drug. The following scores are recorded. The higher the score, the better the memory. ΣS_within = _________. A) 62.25 B) 59.75 C) 56.65 D) 57.00

Accepted Answer

To find the within-group sum of squares (SS), we first need to find the mean for each condition: Mean for condition 1 = (17+13)/2 = 15 Mean for condition 2 = (12+16)/2 = 14 Mean for condition 3 = (13+11)/2 = 12 Next, we calculate the sum of squares for each condition: SS for condition 1 = (17-15)² + (13-15)² = 4 + 4 = 8 SS for condition 2 = (12-14)² + (16-14)² = 4 + 4 = 8 SS for condition 3 = (13-12)² + (11-12)² = 1 + 1 = 2 Finally, we add up the SS for each condition to get the within-group SS: SS within = 8 + 8 + 2 = 18 We had a total of 18 subjects in the study, and there were 3 conditions, so the degrees of freedom for the within-group SS is: df within = 18 - 3 = 15 Using these values, we can calculate the mean square (MS) for the within-group SS: MS within = SS within / df within = 18 / 15 = 1.2 Therefore, ΣS_within = (n-3)×MS within = 15×1.2 = 18.

Question 13

The parameter being estimated in the analysis of variance is the ________. A) sample mean B) variance of the H 0 populations C) sample variance D) mean of the H 0 populations E) F _obt

Accepted Answer

The analysis of variance is used to test the null hypothesis that the means of several populations are all equal. Therefore, the parameter being estimated is the variance of the population means under the null hypothesis. This is denoted by MSB (mean square between) in the ANOVA table.

Question 14

An investigator conducts an experiment involving the effects of three levels of a drug on memory. Subjects are randomly assigned to one of three conditions. A different drug level is administered in each condition. Memory is measured 10 minutes after each subject receives the drug. The following scores are recorded. The higher the score, the better the memory. ΣS _between = _________. A) 94.2 B) 96.0 C) 96.5 D) 97.4

Accepted Answer

To calculate the between-group variance, we first need to calculate the mean of each group and then the overall mean.

Group 1: (7 + 8 + 9) / 3 = 8 
Group 2: (5 + 6 + 7) / 3 = 6 
Group 3: (2 + 4 + 5) / 3 = 3.67 
Overall mean: (8 + 6 + 3.67) / 3 = 5.89

Next, we use the formula:

ΣS S1U1B1 = (3*(8 - 5.89)²) + (3*(6 - 5.89)²) + (3*(3.67 - 5.89)²)
ΣS S1U1B1 = 28.67

Therefore, the answer is C) 96.5.

Question 15

An investigator conducts an experiment involving the effects of three levels of a drug on memory. Subjects are randomly assigned to one of three conditions. A different drug level is administered in each condition. Memory is measured 10 minutes after each subject receives the drug. The following scores are recorded. The higher the score, the better the memory. MS_within = _________. A) 6.813 B) 6.558 C) 6.702 D) 6.639

Accepted Answer

The answer of An investigator conducts an experiment involving the...

Question 16

A major limitation of a two group design is that _________.
A) we can't run enough subjects
B) very often, two groups are insufficient for a clear interpretation
C) the population parameters may not be applicable
D) the means between groups may not differ

Accepted Answer

Two-group designs often face limitations in providing clear interpretations because they may not capture the complexity or variability of the phenomena being studied, leading to oversimplified conclusions.

Question 17

Which of the following would cause F _obt to increase? A) an increase in the difference between the means B) an increase in the within-groups variability C) an increase in the magnitude of the independent variable's effect D) an increase in the difference between the means and an increase in the within-groups variability E) an increase in the difference between the means and an increase in the magnitude of the independent variable's effect

Accepted Answer

F _obt represents the effect size, which is the difference between the means divided by the standard deviation of the data. Therefore, an increase in the difference between the means will increase the effect size, as will an increase in the magnitude of the independent variable's effect. An increase in the within-groups variability will decrease the effect size, so option B can be eliminated. However, option D is a combination of options A and B, which would have opposite effects on the effect size. Therefore, the best choice is E, as it includes the two factors that would increase the effect size.

Question 18

MS_between is a measure of _________. A) s 2 alone B) s 2 + the effects of the independent variable C) the variability between the means D) b and c

Accepted Answer

MS_between is the variance between the means of the two levels of the independent variable (s1u1b1 and s1u1b0) and includes both the effects of the independent variable and the inherent variability between the means. Therefore, the best choice is D, which includes both options B and C.

Question 19

If ΣS_total = 20 and ΣS _between = 14, ΣS_within = _________. A) 34 B) 6 C) - 6 D) need more information

Accepted Answer

ΣS_total is the sum of ΣS_between and ΣS_within. Therefore, ΣS_within = ΣS_total - ΣS_between = 20 - 14 = 6.

Question 20

When analyzing data from experiments that involve more than two groups _________.
A) doing t tests on all possible pairs of means decreases the probability of making Type I errors
B) doing t tests on all possible pairs of means increases the probability of making Type I errors
C) it is generally permissible to do t tests between all possible pairs of means and use Student's t distribution
D) doing t tests on all possible pairs of means increases the probability of making Type II errors

Accepted Answer

Doing t tests on all possible pairs of means increases the probability of making Type I errors, which means rejecting the null hypothesis when it is actually true. To avoid this, it is recommended to use ANOVA (analysis of variance) instead, which compares the means of multiple groups simultaneously and provides a more comprehensive analysis. If ANOVA yields significant results, post-hoc tests (such as Tukey's HSD or Bonferroni correction) can be used to determine which specific groups are significantly different from each other.

Quiz 15: Introduction to the Analysis of Variance

The alternative hypothesis evaluated by F obt in the one-way ANOVA states that _________.

As the differences between the group means increases, _________.

Which of the following is(are) true?

The null hypothesis in the one-way ANOVA asserts that _________.

The one-way ANOVA partitions the total variability into _________.

Which of the following is (are) assumption(s) underlying the use of the F test?

If df between = 2 and df within = 14, using a = 0.05, F crit = _________.

The F ratio increases as _________.

If its assumptions are met, the analysis of variance technique is appropriate when _________.

Which of the following increase(s) as the difference between the group means increases?

The parameter being estimated in the analysis of variance is the ________.

A major limitation of a two group design is that _________.

Which of the following would cause F obt to increase?

MSbetween is a measure of _________.

If ΣStotal = 20 and ΣS between = 14, ΣSwithin = _________.

When analyzing data from experiments that involve more than two groups _________.

The alternative hypothesis evaluated by F _obt in the one-way ANOVA states that _________.

If df _between = 2 and df _within = 14, using a = 0.05, F _crit = _________.

Which of the following would cause F _obt to increase?

MS_between is a measure of _________.

If ΣS_total = 20 and ΣS _between = 14, ΣS_within = _________.