# If the treatment has no effect, we would expect group population means to be equal group sample means to be equal group sample means to vary none of the above

**QUESTION**

- If the treatment has no effect, we would expect

group population means to be equal | ||

group sample means to be equal | ||

group sample means to vary | ||

none of the above |

**QUESTION 2**

- In analysis of variance, problems that tend to be created by nonhomogeneity of variance are

minimized when group sample size is equal for all groups | ||

minimized when group sample size is large | ||

minimized by both (a) and (b) | ||

unaffected by sample size |

**QUESTION 3**

- In analysis of variance, nonnormality of the distribution of group scores

is not likely to be a problem if samples are drawn from different populations | ||

is not a problem | ||

is likely to be a problem only when the number of degrees of freedom for the denominator of F is large | ||

is not likely to be a problem if sample size is large |

**QUESTION 4**

- If we divide a sum of squared deviation scores by the associated degrees of freedom we have

inherent variation | ||

within-groups variation | ||

population variance | ||

variance estimate |

**QUESTION 5**

- Variability of group means about the grand mean affords an indication of

a. | random individual variation | |

b. | variation attributable to treatment effect, when present | |

c. | a combination of (a) and (b) above | |

d. | none of the above |

**QUESTION 6**

- In analysis of variance, if the group sample means were all equal, the calculated value of F would be

greater than +1.00 | ||

+1.00 | ||

zero | ||

negative |

**QUESTION 7**

- In the analysis of variance F test, when the null hypothesis is false, we would expect most calculated values of F to

exceed +1.00 | ||

be zero | ||

+1.96 when α=.05 | ||

be between zero and +1.00 |

**QUESTION 8**

- In one-way analysis of variance involving three groups, the alternative hypothesis would be considered correct if, in the population,

all means were equal | ||

two means are equal but the third is different | ||

all three means have different values | ||

either (b) or (c) above is true |

**QUESTION 9**

- The assumption of homogeneity of variance means that

group population variance should be the same for all groups | ||

within-group variance should be the same as total variance | ||

within-group variance should be the same as between-group variance | ||

between-group variance should be the same as total variance |

**QUESTION 10**

- The F distribution is like the t distribution in that

it is symmetrical | ||

both positive and negative values are possible | ||

its mean is zero | ||

it is actually a family of distributions |

**QUESTION 11**

- In the analysis of variance F test, the quantity that reflects the treatment effect

is sometimes placed in the numerator and sometimes in the denominator | ||

is always placed in the numerator | ||

is excluded from F | ||

is always placed in the denominator |

**QUESTION 12**

- It is appropriate and necessary to run post-hoc comparisons under what conditions?

The F statistic is not significant, but we suspect there might be a significant difference between two groups. | ||

The F statistic is not significant. | ||

The F statistic is significant. | ||

There are two groups in the analysis. |

**QUESTION 13**

- F is formed by

the difference between two variance estimates | ||

the difference between two standard deviation estimates | ||

the ratio between two variance estimates | ||

the ratio between two population variances |

**QUESTION 14**

- Which, if any, is not a characteristic necessary for F to be distributed according to its tabled values?

group populations are normally distributed | ||

the numerator and denominator estimates are independent | ||

sampling is random | ||

sample group means are equal |

**QUESTION 15**

- If there are n scores in each group and k groups, the between-groups variance estimate is calculated by dividing the appropriate sum of squares by

n-k | ||

n-1 | ||

Sum(n-1) | ||

k-1 |

**QUESTION 16**

- The denominator of any variance estimate consists of

inherent variation | ||

sums of squared deviations | ||

degrees of freedom | ||

within-groups variation |

**QUESTION 17**

- If we run a one-way ANOVA on three groups, which of these outcomes are possibly true?

Group A is significantly different from Group B, but there is no significant difference between Groups B and C. | ||

Group A is significantly different from Group B, but there is no significant difference between Groups A and C. | ||

All three groups are significantly different from all the other groups. | ||

All of the above are possibly true outcomes. |

**QUESTION 18**

- What does the effect size (η
^{2}) in an ANOVA tell us?

How much of the total variance is between-groups variance. | ||

The magnitude of the total variance. | ||

How far apart the means of the groups are. | ||

How much of the total variance is within-groups variance. |

**QUESTION 19**

- One-way analysis of variance is applicable when there are

at least five groups | ||

no more than five groups | ||

at least two groups | ||

at least three groups |

**QUESTION 20**

- The obtained values of chi-square

can be negative even if no discrepancy is negative | ||

cannot be as low as zero | ||

can be negative if discrepancies have negative values | ||

can be no lower than zero |

**QUESTION 21**

- Older texts recommended using a “correction for continuity” when df=1 particularly if fe in one of the categories was less than 5. However, more recent studies have shown that the uncorrected chi-square is reasonably accurate when

all f_{e}‘s are at least 2 |
||

all f_{e}‘s are at least 3 |
||

the average f_{e} is at least 5 |
||

the average f_{e} is at least 2 |

**QUESTION 22**

- For a particular category, we find the difference between expected and observed frequency to differ by 25 points. This will tend to make chi-square large if

the difference is positive | ||

f_{e} is small |
||

f_{o} is small |
||

the difference is negative |

**QUESTION 23**

- For a given level of significance, the critical value of chi-square will be larger

when the number of categories is smaller | ||

when the number of degrees of freedom is smaller | ||

when the number of degrees of freedom is larger | ||

when n is larger |

**QUESTION 24**

- In the chi-square test, a very low (close to 0) value of chi-square implies that

the observed frequencies are more like their corresponding expected frequencies than would be expected by chance | ||

the several observed frequencies are very similar | ||

the positive difference between expected and observed frequencies tend to balance the negative differences | ||

the several expected frequencies are very similar |

**QUESTION 25**

- In the chi-square test, we will reject the null hypothesis if the obtained chi-square is

close to the mean of the tabled distribution of chi-square | ||

either very low or very high | ||

very low | ||

very high |

**QUESTION 26**

- Which, if any, is not a characteristic necessary for obtained values of chi-square to be distributed according to the tabled values of the chi-square distribution?

expected frequencies must be equal for all groups | ||

the null hypothesis must be true | ||

sampling must be random | ||

all of the above must be true |

**QUESTION 27**

- Only red and blue flowers are produced from a particular seed mixture. We plant a random sample of 27 seeds and obtain 6 blue and 21 red flowers. We wish to test the null hypothesis that the mixture gives twice as many red flowers as blue flowers. The value of fe for red flowers is

18 | ||

13 1/2 | ||

16 | ||

9 |

**QUESTION 28**

- In a chi-square goodness-of-fit problem, there are 6 categories, and expected frequencies of 5 in each category. The number of degrees of freedom for this problem is

5 | ||

24 | ||

29 | ||

25 |

**QUESTION 29**

- In one chi-square problem, each observed frequency was the same as its expected frequency.

This would be an unusual result even if the null hypothesis were true. | ||

This would be an unusual result even if the null hypothesis were false. | ||

Chi-square will be zero. | ||

All of the above are true. |

**ANSWER**

Here are the answers to the provided questions:

QUESTION 1: group sample means to vary

QUESTION 2: minimized when group sample size is equal for all groups

QUESTION 3: is likely to be a problem only when the number of degrees of freedom for the denominator of F is large

QUESTION 4: variance estimate

QUESTION 5: a combination of (a) and (b) above

QUESTION 6: zero

QUESTION 7: exceed +1.00

QUESTION 8: either (b) or (c) above is true

QUESTION 9: group population variance should be the same for all groups

QUESTION 10: it is actually a family of distributions

QUESTION 11: is sometimes placed in the numerator and sometimes in the denominator

QUESTION 12: The F statistic is significant.

QUESTION 13: the ratio between two variance estimates

QUESTION 14: group populations are normally distributed

QUESTION 15: n-1

QUESTION 16: within-groups variation

QUESTION 17: All of the above are possibly true outcomes.

QUESTION 18: How much of the total variance is between-groups variance.

QUESTION 19: at least two groups

QUESTION 20: can be no lower than zero

QUESTION 21: all fe’s are at least 5

QUESTION 22: the difference is positive

QUESTION 23: when the number of degrees of freedom is smaller

QUESTION 24: the observed frequencies are more like their corresponding expected frequencies than would be expected by chance

QUESTION 25: very high

QUESTION 26: expected frequencies must be equal for all groups

QUESTION 27: 16

QUESTION 28: 5

QUESTION 29: Chi-square will be zero.

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