Question 1

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

Accepted Answer

Degrees of freedom is a term used in statistics that refers to the number of values in a calculation that can vary without violating any constraints. In the case of sample variance, the degrees of freedom is equal to the sample size minus one, which is represented by the expression N - 1. Therefore, choice A is the correct representation of degrees of freedom.

Question 2

What is the effect size for the cancer survival data?

Accepted Answer

The effect size for the cancer survival data is 0.9, which indicates a large effect size.

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.)

Accepted Answer

A boxplot can help identify outliers, central tendencies, and the spread of the data. A histogram can help visualize the distribution of the data, including the shape and any potential deviations from normality. Pie charts and scatterplots are not appropriate for presenting data for a t-test.

Question 4

Analyse the heart rate data collected during a VO₂max 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.

Accepted Answer

The answer of Analyse the heart rate data collected during...

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.)

Accepted Answer

The answer of Examine the following SPSS output from the...

Question 6

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

Accepted Answer

Survival rate (days) can be classified as a ratio scale because the zero point (no survival) is meaningful, the intervals between values are equal, and there is a true and meaningful ratio between different survival rates (e.g. surviving for 10 days is twice as long as surviving for 5 days).

Question 7

How is a t-statistic calculated?

Accepted Answer

The t-statistic is calculated by dividing the difference between the means of two groups by the standard error of the mean, which measures the variability of the sample means around the true population mean. The larger the difference between the means and the smaller the standard error, the larger the t-value, indicating a greater likelihood that the observed difference is not due to chance.

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?

Accepted Answer

The answer of Assume that for the research into stomach...

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?

Accepted Answer

Cohen's d is calculated as the difference between the means of two groups divided by the pooled standard deviation. The formula for Cohen's d is (mean 2 - mean 1) / mean of the standard deviation.

Question 10

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

Accepted Answer

The variable labeled as cancer is a categorical variable that represents a type of disease. It cannot be ranked or ordered in any meaningful way; hence, nominal measurement scale is the best choice for this variable.

Question 11

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

Accepted Answer

The correct result for the independent t-test is A because it shows a statistically significant result with p = .038, which is less than the common alpha level of 0.05.

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?

Accepted Answer

The answer of Analyse the data below related to days...

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?

Accepted Answer

A Levene's test is used to test the equality of variances across different groups. A p-value of .006 indicates that the variances of the stomach and lung cancer groups are significantly different from each other, therefore violating the assumption of equal variances needed for an independent t-test. Thus, we can infer that the variance is heterogeneous.

Question 14

What does a negative t-statistic suggest?

Accepted Answer

A negative t-statistic suggests that the group being compared has a mean that is lower than the other group. In this case, since the lung cancer mean was subtracted from the stomach cancer mean, a negative t-statistic would suggest that the lung cancer group has a lower mean than the stomach cancer group. Choice A suggests the opposite direction of subtraction, and choice C is not relevant as SPSS does not randomly order numbers in t-tests. Choice D is incorrect as there is a clear answer to this question.

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?

Accepted Answer

To convert a two-tailed significance level (p) to a one-tailed significance level, we divide it by 2. Therefore, for p = .284, dividing it by 2 would give us the new significance level for a one-tailed test, which is .142 (option A). The other options are incorrect as they do not follow the correct method for converting two-tailed significance to one-tailed significance.

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?

Accepted Answer

Since the scores for the novice group are not normally distributed, we cannot run an independent t-test. The Mann-Whitney test is a nonparametric test that does not assume normality, making it suitable for comparing two groups with non-normally distributed data. Therefore, the Mann-Whitney test is the best choice to test for statistical differences between the novice and expert tennis players' pre-competition arousal scores.

Question 17

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

Accepted Answer

A p-value of .000 is typically reported as p < .001, indicating that the result is highly significant and the probability of the result occurring by chance is less than 0.1%.

Question 18

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

Accepted Answer

The independent t-test is used for comparing the means of two separate groups, while the other tests (paired-samples, matched-pairs, dependent) are used for comparing means within the same group or related groups.

Question 19

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

Accepted Answer

Mixed model t-test is not a form of t-test. Rather, it is a type of statistical analysis used for repeated measures or mixed designs where there are both within-subject and between-subject factors.

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?

Accepted Answer

The answer of When analysing the result of the paired...

Quiz 10: Comparing Two Means