Question 1

A researcher was interested in stress levels of lecturers during lecturers. She took the same group of 8 lecturers and measured their anxiety (out of 15) during a normal lecture and again in a lecture in which she had paid students to be disruptive and misbehave. Based on the SPSS output, how would you interpret these results?

Accepted Answer

The output indicates a significant difference in anxiety levels between normal lectures and lectures in which students misbehaved, with a p-value of 0.002 (smaller than the 0.05 standard for significance). The mean anxiety level during normal lectures was 4.13, while during lectures with disruptive students it was 8.25, indicating a clear increase in anxiety levels.

Question 2

An paired-samples t-test is used to test for:

Accepted Answer

A paired-samples t-test is used to compare the means of two related groups, where the same entities are measured twice under different conditions. The test assumes that the sampling distribution is normally distributed, and the data have equal variances and are at least interval. Therefore, option B is the correct choice. Option A refers to an independent-samples t-test, while option C and D introduce other factors that are not relevant to a paired-samples t-test.

Question 3

The t-statistic:

Accepted Answer

The t-statistic is the ratio of systematic variation (the difference between group means) to unsystematic variation (the variation within groups). It is an important measure in hypothesis testing, particularly in comparing means between two groups.

Question 4

What does the independent t-test test assume?

Accepted Answer

The answer of What does the independent t-test test assume?
...

Question 5

A recent study investigated whether vodka is less likely to give you a hangover than wine. Twenty participants on a night out were asked to drink only vodka for the whole evening then rate how they felt the next day out of 10 (0 = I feel fantastic, 10 = I can't move my head in case it explodes). The following month, they were asked to do the same again, only this time they were asked to drink only white wine. The t-score was 2.56. Which of the sentences below is correct?

Accepted Answer

The t-score of 2.56 corresponds to a p-value of about 0.0145 (using a two-tailed test with 19 degrees of freedom). This means that there is evidence to suggest that there is a difference in hangover ratings between drinking only vodka versus drinking only white wine. Since the p-value is less than 0.05 (i.e. 5%), the result is significant at the 5% level. However, it is not significant at the 1% level (i.e. p-value is greater than 0.01). Therefore, choice C is the correct answer.

Question 6

A small standard error of differences tells us:

Accepted Answer

A small standard error of differences indicates that the sample means are tightly clustered around the population mean, so most pairs of samples will have very similar means. This suggests that the differences between pairs of samples are not due to random chance, but rather reflect true differences in the population.

Question 7

Participants rated their mood score out of 20 before and after listening to Reign in Blood by the thrash metal band Slayer. $\begin{array} { | c | c | } 
\hline \text { Before Listening to Slayer } & \text { After Listening to } \mathbf { S l a y e r } \
\hline 5 & 14 \
\hline \mathbf { 8 } & \mathbf { 5 } \
\hline \mathbf { 9 } & 17 \
\hline 4 & 18 \
\hline \mathbf { 3 } & \mathbf { 8 } \
\hline 15 & 19 \
\hline 12 & 14 \
\hline \mathbf { 6 } & 16 \
\hline
\end{array}$ 
- What is the null hypothesis of this study?

Accepted Answer

The null hypothesis typically states that there is no effect or no difference. In this context, it means that listening to Slayer does not affect mood score, implying no change in mood as a result of listening to the music.

Question 8

The degrees of freedom for the paired samples t-test are:

Accepted Answer

The degrees of freedom for the paired samples t-test is determined by the number of pairs of observations minus 1. Therefore, the formula for the degrees of freedom is N-1, where N is the number of pairs of observations. Choice C represents this formula, while the other choices include incorrect calculations or additional variables that are not relevant to determining the degrees of freedom.

Question 9

A researcher measured a group of people's physiological reactions while watching horror films and compared them to when watching comedy films. The resulting data were normally distributed. What test should be used to analyse the data?

Accepted Answer

A paired-samples (dependent or related) t-test is appropriate when comparing the same group of participants' physiological reactions to both the horror and comedy films. This is because the data are normally distributed, and the participants are being compared to themselves in two different conditions.

Question 10

Which of the following statements about the t distribution is correct?

Accepted Answer

As the degrees of freedom increase, the t distribution becomes closer in shape to the normal distribution. This is due to the central limit theorem, which states that as sample size increases, the distribution of the sample means will approach a normal distribution.

Question 11

A researcher was interested in the effects of emotion-evoking music on exam performance. Before their SPSS exam, a lecturer took one group of students to a room in which calming music was being played. A different group of students were taken to another room in which the 'death march' was being played. The students then did the exam and their marks were noted. The SPSS output is below. The experimenter made no predictions about which form of support would produce the best exam performance. What should he report? $\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\text { Group Statistics }$
$\begin{array}{l}
\begin{array} { | l l | r | r | r | r | } 
\hline & \text { Emotional Support } & { \mathrm { N } } &{ \text { Mean } } &  { \begin{array} { c } 
\text { Std. } \
\text { Deviation }
\end{array} } & { \begin{array} { c } 
\text { Std. Error } \
\text { Mean }
\end{array} } \
\hline \text { SPSS Exam Mark } & \text { Positive Support } & 20 & 65.1500 & 5.0396 & 1.1269 \
& \text { Negative Support } & 20 & 57.8000 & 15.2129 & 3.4017 \
\hline
\end{array}
\end{array}$

Accepted Answer

The answer of A researcher was interested in the effects...

Question 12

Which of the following sentences is an accurate description of the standard error?

Accepted Answer

The standard error is the standard deviation of the sampling distribution of a statistic. It measures the variation of the sampling distribution around the true population parameter.

Question 13

An independent t-test is used to test for:

Accepted Answer

An independent t-test is used to test for differences between means of groups containing different entities when the sampling distribution is normal, the groups have equal variances and data are at least interval. This means that the data has a normal distribution, the variances are equal across groups being compared, and the data is measured at an interval or ratio level. If these assumptions are not met, other tests like the Mann-Whitney U test or Welch's t-test may be more appropriate.

Question 14

When conducting an independent t-test, what is the dependent variable?

Accepted Answer

In an independent t-test, the dependent variable is the score of the participants being compared across two independent groups. The independent variable is the group membership (experimental conditions). Therefore, the correct choice is D, "The scores". Choice A is incorrect because the concept of dependent variable is applicable to the t-test. Choice B is incorrect as one cannot have an independent variable becoming the dependent variable. Choice C is incorrect because experimental conditions are the independent variable under investigation.

Question 15

Participants rated their mood score out of 20 before and after listening to Reign in Blood by the thrash metal band Slayer. $\begin{array} { | c | c | } 
\hline \text { Before Listening to Slayer } & \text { After Listening to } \mathbf { S l a y e r } \
\hline 5 & 14 \
\hline \mathbf { 8 } & \mathbf { 5 } \
\hline \mathbf { 9 } & 17 \
\hline 4 & 18 \
\hline \mathbf { 3 } & \mathbf { 8 } \
\hline 15 & 19 \
\hline 12 & 14 \
\hline \mathbf { 6 } & 16 \
\hline
\end{array}$ 
-What are the degrees of freedom for this study?

Accepted Answer

The degrees of freedom for a paired-samples t-test is n-1, where n is the number of pairs of scores. In this case, there are 8 pairs of scores, so the degrees of freedom is 8-1 = 7.

Question 16

Two samples of data are collected and the sample means calculated. If the samples come from the same population, then:

Accepted Answer

If two samples come from the same population, then we would expect their means to be roughly equal. This is because the samples should reflect the same underlying population, so the means should be similar. If the means differ significantly, it suggests that the two samples may come from different populations. Option B, D and C are incorrect because the means of two samples from the same population should not differ significantly, the difference between the samples should be within the expected range of standard error, and the reliability of the experiment is not in question here.

Question 17

Other things being equal, compared to the paired-samples (or dependent) t-test, the independent t-test:

Accepted Answer

The independent t-test generally has less power than the paired-samples t-test because it does not account for the correlation between paired observations, which can reduce variability and increase power in the paired-samples t-test.

Question 18

If you use a paired samples t-test:

Accepted Answer

All three options are correct. In a paired samples t-test, the same participants take part in both conditions, which reduces individual differences and hence unsystematic variance. As a result, paired samples designs typically require fewer participants than independent samples designs.

Question 19

A psychologist was interested in whether there was a gender difference in the use of email. She hypothesized that because women are generally better communicators than men, they would spend longer using email than their male counterparts. To test this hypothesis, the researcher sat by the email computers in her research methods laboratory and when someone started using email, she noted whether they were male or female and then timed how long they spent using email (in minutes). What should she report? $\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\text { Group Statistics }$
$\begin{array}{|ll|r|r|r|r|} 
\hline & \text { Gender } & \mathrm{N} & \text { Mean } & \text { Std. Deviation } & {\begin{array}{c}
\text { Std. Error } \
\text { Mean }
\end{array}} \
\hline \text { Time Using Email (Day 2) } & \text { Male } & 8 & 5.0000 & 4.50397 & 1.59239 \
& \text { Female } & 8 & 32.0000 & 40.04640 & 14.15854\
\hline 
\end{array}$

Accepted Answer

The answer of A psychologist was interested in whether there...

Question 20

What does the variance sum law state?

Accepted Answer

The variance sum law states that the variance of a difference between two independent variables is equal to the sum of their variances. This can be expressed mathematically as Var(X-Y) = Var(X) + Var(Y), where X and Y are independent variables.

Quiz 10: Comparing Two Means