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.