Deck 10: Comparing Two Means

Question 1

Which of the following expressions best represents the degrees of freedom?

A) N - 1
B) N + 1
C) N - 2
D) N + 2

Answer 1

A

Question 2

What is the effect size for the cancer survival data?

A) 0.9
B) 0.6
C) 0.3
D) 0.1

Answer 2

A

Question 3

When exploring the data before performing a t-test, how might you wish to present the data graphically? (You may select more than one option.)

A) Boxplot
B) Pie chart
C) Histogram
D) Scatterplot

Answer 3

A AND C

Question 4

Analyse the heart rate data collected during a VO₂ max test. The data points (observations) were collected at the point the lactate threshold occurred (the point at which blood lactate deviates from resting concentrations) before and after a six-week aerobic training programme. Interpret the SPSS output and decide whether the two data sets are normally distributed.

A) Both pre- and post-test data sets are normally distributed.
B) The pre-test data set is normally distributed but the post test data set is not.
C) The post-test data set is normally distributed but the pre-test data set is not.
D) Neither data set is normally distributed.

Question 5

Examine the following SPSS output from the heart rate data. Based on 11 degrees of freedom, working to a two-tailed significance value of .05, the critical value for t is 2.201. What can you assume from the output? (The significance value has been omitted on purpose.)

A) The data sets were not significantly different.
B) The data sets were significantly different.
C) The critical value and the t-statistic were too similar and therefore inconclusive.
D) The data sets are most likely normally distributed.

Question 6

How might you classify the measurement scale of the survival rate (days)?

A) Nominal
B) Ordinal
C) Interval
D) Ratio

Question 7

How is a t-statistic calculated?

A) Mean difference / standard error of the mean
B) Mean difference / standard deviation
C) Standard error of the mean / standard deviation
D) Standard deviation / degrees of freedom

Question 8

Assume that for the research into stomach and lung cancer the significance value is set at p < .05 and an independent t-test yielded a significance value of p = .06. What should you do?

A) Accept the null hypothesis and state that there is no difference in the duration of the survival between the two types of cancer.
B) Reject the null hypothesis and state that there is a difference in the duration of the survival between the two types of cancers.
C) Accept the null hypothesis and state that there is no difference in the duration of the survival between the two types of cancer, but that it is worth further investigation.
D) The results are inconclusive.

Question 9

Once you have the significance value of the t-test, it is beneficial to calculate the effect size. Cohen's d is a measure of effect size. How is it calculated?

A) (mean 2 - mean 1) / mean of the standard deviation
B) (mean 2 - mean 1) × mean of the standard deviation
C) (mean 2 + mean 1) - mean of the standard deviation
D) (mean 2 / mean 1) + mean of the standard deviation

Question 10

How might you classify the measurement scale for the variable labelled as cancer?

A) Nominal
B) Ordinal
C) Interval
D) Ratio

Question 11

What is the correct result for the independent t-test?

A) t_(17.95) = -2.24, p = .038
B) t₍₂₈₎ = -1.98, p = .058
C) t_(17.95) = -2.24, p = .006
D) t₍₂₈₎ = -1.98, p = .006

Question 12

Analyse the data below related to days survival following surgery from either stomach or lung cancer. What is the result of the Kolmogorov-Smirnov test for the patients who survived stomach cancer?

A) D(13) = .203, p = .146
B) D(17) = .175, p = .173
C) D(13) = .930, p = .344
D) D(17) = .821, p = .004

Question 13

Run an independent t-test on the data. A Levene's test result of p = .006 was obtained. What can we infer from this number?

A) The stomach and lung cancer variance is heterogeneous.
B) The stomach and lung cancer variance is homogenous.
C) The distributions look fairly similar.
D) The result is inconclusive.

Question 14

What does a negative t-statistic suggest?

A) The stomach cancer mean was subtracted from the lung cancer mean.
B) The lung cancer mean was subtracted from the stomach cancer mean.
C) It is impossible to tell as SPSS randomly orders the numbers.
D) None of the above.

Question 15

Suppose we wanted to apply a one-tailed test as opposed to a two-tailed test. How would we covert a significance of p = .284?

A) .284 / 2 = .142
B) .284 × 2 = .568
C) .284 / 11 = .026
D) .284 × 11 = 3.124

Question 16

When comparing pre-competition arousal scores in novice and expert tennis players you find that the scores for the novice group are not normally distributed. What test should be run to see if arousal scores are statistically different?

A)Independent t-test
B) Mann-Whitney test
C) Paired-samples t-test
D) Wilcoxon test

Question 17

If a significance result of .000 is presented, how should this be reported?

A) p = .000
B) p < .000
C) p < .001
D) p > .001

Question 18

Which of the following t-tests has a different research design?

A) Independent t-test
B) Paired-samples t-test
C) Matched-pairs t-test
D) Dependent t-test

Question 19

Which of the following is not a form of t-test?

A) Independent-samples t-test
B) Paired-samples t-test
C) One-sample t-test
D) Mixed model t-test

Question 20

When analysing the result of the paired samples t-test, the output presents the following box, but what do the results show you?

A) The correlation value between the two variables is strong, statistically significant and therefore correct to use.
B) The correlation value between the two variables is moderate, but not statistically significant and therefore should not have been used.
C) The correlation value between the two variables is weak and not statistically significant and therefore should not have been used.
D) The correlation value between the two variables is weak, but statistically significant and therefore correct to use.

Question 21

When analysing the cancer survival data, a p-value set at .05 or .01 is most likely to protect against which type of error?

A) Type I error
B) Type II error
C) Type I and II errors
D) It is sufficient to protect against either error.

Question 22

According to Cohen, how might this effect size be interpreted?

A) Large effect size
B) Medium effect size
C) Small effect size
D) Very small effect size

Question 23

Which of the following statements best reflects statistical power?

A) The ability of a statistical test to detect a difference when one genuinely exists.
B) The ability of a statistical test to yield appropriate participant numbers.
C) The ability of a statistical test to successfully identify the confidence intervals of a sample mean.
D) The ability of a statistical test to apply a meaningful effect.

Question 24

Which of the following issues are likely to cause Type II error in the cancer survival data?

A) Error in recording the survival rate
B) Small sample size resulting in insufficient power
C) Treatment effect poorly applied
D) All of the above