Data Handling: Inferential Statistics (AQA A Level Psychology)

A psychology teacher read a researcher’s study on sport and happiness. She considered whether setting group tasks could improve her students’ level of happiness. She decided to conduct an independent groups experiment with 30 students taking A-level Psychology using the same happiness questionnaire.

Suggest an appropriate statistical test the psychology teacher could use to analyse the data. Justify your choice of test.

A researcher investigated whether there was a correlation between the number of hours slept and how well rested the students felt.

The researcher randomly selected 18 participants from first-year students at the university.

On the day of the study, each student participant was asked, ‘How many hours did you sleep last night?’ They then had to rate on a scale of 1 to 5 how well rested they felt.

The researcher hypothesised that there would be a positive correlation between the two co-variables.

The researcher used Spearman’s rho statistical test to analyse the data from this study.

Explain why Spearman’s rho was a suitable test for this study. Refer to the description of the study in your answer.

The researcher chose to use the 5% level of significance and the calculated correlation box coefficient for the Spearman’s rho test was 0.395

Table 1 Critical values of rho

The calculated value of rho must be greater than or equal to the critical value to be significant.

Identify the appropriate critical value from Table 1. Explain your choice.

Explain whether the researcher’s hypothesis should be accepted. Refer to the critical value identified in Question 2b in your answer.

Explain why the researcher decided to use the 5% level of significance rather than the 1% level in this study.

When the researcher compared the calculated and critical values of rho, he began to wonder if he might have made a Type II error.

Explain what is meant by a Type II error in the context of this study.

A researcher studying depression wanted to see whether or not there was a relationship between level of self-esteem and negative schema score. She constructed two questionnaires and asked ten people who had been diagnosed with depression to complete them.

One questionnaire measured the participant’s level of self-esteem. A low score (out of 50) indicated low self-esteem.

The other questionnaire measured whether the participant showed evidence of negative schema. A low score (out of 50) indicated evidence of negative schema. The two sets of results for each participant are shown in the table below.

The researcher analysed the data in Table 1 using a Spearman’s rho statistical test.

Table 1 Self-esteem score and negative schema score for each patient

With reference to level of measurement, explain why Spearman’s rho is an appropriate statistical test for this data.

A biological psychologist wanted to see if there was a positive correlation between heart rate (measured in beats per minute) and levels of a stress hormone (measured in micrograms) in people with obsessive-compulsive disorder (OCD). She wrote a directional hypothesis and collected data from 20 people with OCD.

The psychologist chose to use the Pearson’s r test to analyse the data because she was testing for a correlation. The calculated value of r for the Pearson’s test was +0.42.

The researcher used the following table of critical values.

Calculated value of r must be equal to or more than the critical value for significance to be shown Degrees of freedom (df) = N – 2

Is the psychologist’s calculated value significant? With reference to Table 1, explain your answer.

In an experiment, researchers arranged for participants to complete a very personal and embarrassing questionnaire in a room with other people. Each participant was tested individually. The other people were confederates of the experimenter.

In condition 1: the confederates completed the questionnaire.

In condition 2: the confederates refused to complete the questionnaire and asked to leave the experiment.

The researchers tested 15 participants in condition 1, and 15 different participants in condition 2.

The researchers recorded the number of participants who completed the questionnaire in each condition.

In order to analyse the difference in the number of participants who completed the questionnaire in each condition, the researchers used a chi-squared test.

Apart from reference to the level of measurement, give two reasons why the researchers used the chi-squared test.

The calculated value of chi-squared in the experiment described as 3.97

Table 1: Critical values for the chi-squared test

The calculated value of chi-squared should be equal to or greater than the critical value to be statistically significant.

With reference to the critical values in Table 1, explain whether or not the calculated value of chi-squared is significant at the 5% level.

In 1987, a survey of 1000 young people found that 540 said they smoked cigarettes, whilst 460 said they did not. In 2017, a similar survey of another 1000 young people found that 125 said they smoked cigarettes, whilst 875 said they did not.

Which statistical test should be used to calculate whether there is a significant difference in reported smoking behaviour between the two surveys? Give three reasons for your answer.

In an experiment into the effects of cognitive priming, 20 participants played an unfamiliar computer game. Half of the participants watched a violent film before playing the computer game.

The other half watched a neutral film before playing the computer game. After playing the computer game, each participant was classified as showing High Aggression or Low Aggression.

The researcher decided to use a Chi-Squared test to analyse the data from this study. One reason for choosing this test was that each participant only took part in one condition of the experiment.

Referring to information about the study, explain two other reasons why it was appropriate to use a Chi-Squared test in this case.

A psychologist wanted to see if verbal fluency is affected by whether people think they are presenting information to a small group of people or to a large group of people.

The participants were told that they would be placed in a booth where they would read out an article about the life of a famous author to an audience. Participants were also told that the audience would not be present, but would only be able to hear them and would not be able to interact with them.

There were two conditions in the study, Condition A and Condition B.

Condition A: 10 participants were told the audience consisted of 5 listeners.

Condition B: the other 10 participants were told the audience consisted of 100 listeners.

Each participant completed the study individually. The psychologist recorded each presentation and then counted the number of verbal errors made by each participant.

The results of the study are given in Table 1.

Table 1: Mean number of verbal errors and standard deviations for both conditions

Name an appropriate statistical test that could be used to analyse the number of verbal errors in Table 1. Explain why the test you have chosen would be a suitable test in this case.

The psychologist found the results were significant at p<0.05. What is meant by ‘the results were significant at p<0.05’?

A researcher wanted to see whether cognitive behaviour therapy was an effective treatment for depression. Twenty depressed patients who had all recently completed a course of cognitive behaviour therapy were involved in the investigation. From their employment records, the researcher kept a record of the number of absences from work each patient had in the year following their treatment. This was compared with the number of absences from work each patient had in the year prior to their treatment.

Those patients who had fewer absences from work in the year following their treatment than in the year prior to their treatment were classified as ‘improved’ (+).Those patients who had more absences were classified as ‘deteriorated’ (-). Those patients who had the same number of absences were classified as ‘neither’ (0).

The results of the investigation are included in Table 1 below.

The researcher decided to use the sign test to analyse the data.

Explain two factors that the researcher had to take into account when deciding to use the sign test. Refer to the investigation above in your answer.

Calculate the sign test value of s for the data in Table 1 on the previous page. Explain how you reached your answer.

Table 2: Critical values for the sign test

For significance, the value of the less frequent sign is equal to or less than the value of the table.

With reference to the critical values in Table 2, explain whether or not the value of s that you calculated in response to question 6b is significant at the 0.05 level for a two-tailed test.

Researchers were interested in the spatial awareness skills of motorists. They decided to investigate a possible relationship between different aspects of spatial awareness. Motorists who had between ten and twelve years of driving experience and held a clean driving licence with no penalty points were asked to complete two sets of tasks.

Set 1: To follow a series of instructions and using a map, to identify various locations correctly. This provided a map reading score for each motorist with a maximum score of 20.

Set 2: To complete a series of practical driving tasks accurately. This involved tasks such as driving between cones, driving within lines and parking inside designated spaces. Each motorist was observed completing the Set 2 tasks by a single trained observer who rated each performance by giving the driver a rating out of 10.

The following results were obtained.

Table 1: The map reading scores and driver ratings of motorists

The researchers decided to analyse the data using a Spearman’s rho test. Explain why this is a suitable choice of test for this investigation.

After analysis of the data the researchers obtained a calculated value of rs= 0.808.

Using the information in Table 2 above, what conclusion can the researchers draw about the relationship between the map reading and driving skills of the motorists? Explain your answer.

Distinguish between a Type I error and a Type II error.

A psychologist wanted to test whether listening to music improves running performance.

The psychologist conducted a study using 10 volunteers from a local gym. The psychologist used a repeated measures design. Half of the participants were assigned to condition A (without music) and half to condition B (with music).

All participants were asked to run 400 metres as fast as they could on a treadmill in the psychology department. All participants were given standardised instructions. All participants wore headphones in both conditions. The psychologist recorded their running times in seconds. The participants returned to the psychology department the following week and repeated the test in the other condition.

The researcher used a directional hypothesis and analysed the data using a related t-test. The calculated value of t where degrees of freedom (df) = 9 was 1.4377. He decided to use the 5% level of significance.

Table 1 Table of critical values of t

Calculated value of t must be equal to or greater than the critical value in this table for significance to be shown.

Give three reasons why the researcher used a related t-test in this study and, using Table 1, explain whether or not the results are significant.

A psychologist decided to design an experiment to test the effects of recreational screen time on children’s academic performance.

The psychologist randomly selected four schools from all the primary schools in her county to take part in the experiment involving Year 5 pupils. Three of the four schools agreed to take part. In total, there were 58 pupils whose parents consented for them to participate. The 58 pupils were then randomly allocated to Group A or Group B.

For the two-week period of the experiment, pupils in Group A had no recreational screen time. Pupils in Group B were allowed unrestricted recreational screen time. At the end of the experiment all pupils completed a 45-minute class test, to achieve a test score.

The psychologist wanted to test the statistical significance of the data.

Identify the most appropriate choice of statistical test for analysing the data collected and explain three reasons for your choice in the context of this study.

Researchers investigated whether the experience of bullying is influenced by attachment type. They interviewed teenagers about their early attachment experiences. Following the interviews, the teenagers were categorised into two groups based on their attachment type:

• Group 1 – secure attachment in childhood

• Group 2 – insecure attachment (insecure-avoidant or insecure-resistant) in childhood.

During the interview, the teenagers were also asked about their experience of bullying. They were categorised as either:

• having had experience of bullying, or

• having had no experience of bullying.

Which statistical test would be most suitable to analyse the data in this investigation? With reference to this investigation, explain three reasons for your choice of test.

A controlled observation was designed to compare the social behaviours of pre-school children of working parents and pre-school children of stay-at-home parents. The sample consisted of 100 children aged three, who were observed separately. Half of the children had working parents and the other half had stay-at-home parents.

The observation took place in a room which looked like a nursery, with a variety of toys available. In the room, there were four children and one supervising adult. Their behaviour was not recorded.

Each child participant was brought into the room and settled by their parent. The parent then left to sit outside. Each child participant’s behaviour was observed covertly for five minutes while they played in the room.

The observation was conducted in a controlled environment and a standardised script was used when the children and their parents arrived

The data from the observation was summarised by converting the number of agreed observations into a total social behaviour score for each child.

The researcher then conducted a statistical test to identify whether there was a significant difference between the social behaviour scores for the children of stay-at-home parents and those of working parents.

Identify an appropriate statistical test that the researcher could use to analyse the social behaviour scores in this study. Explain three reasons for your choice in the context of this study.