Inferential testing

In an investigation into the accuracy of eyewitness testimony, 40 participants were shown the same film of a car crash.

Following the film, they were randomly allocated to one of two conditions. Each participant was interviewed separately and was asked one critical question.

In Condition A, 20 participants were asked: ‘Did you see the set of traffic lights, Yes or No?’

In Condition B, the other 20 participants were asked: ‘Did you see a set of traffic lights, Yes or No?’

There was no set of traffic lights in the film.

The researcher chose to use a chi-squared statistical test to see whether there was a significant difference in responses to the critical question in the two conditions.

Explain three reasons for this choice with reference to this investigation.

Identify an appropriate statistical test to analyse the data collected in this study. Explain three reasons for your choice.

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The researcher found that the difference in results between the two groups was significant at p<0.01

Explain what is meant by ‘significant at p<0.01’ in the context of this study.

The researcher noticed that a lot of the children who did well on the musical ability test also seemed to do well on the motor skills test.

Suggest how the researcher could use the existing data to investigate the relationship between musical ability and motor skills.

A researcher wanted to test if there is a relationship between the passage of time and recall of nonsense words. They gave 30 participants 40 nonsense words to learn, then tested recall at fixed intervals over several weeks. The nonsense words were standardised to ensure they were of similar difficulty and length.

When writing up the investigation, the researcher represented their data on a scattergram.

Briefly explain how the use of inferential statistics would improve this investigation.

Suggest an appropriate statistical test to improve this investigation. With reference to the study, outline two reasons for your choice of test.

The researcher decided to use an unrelated t-test to analyse the raw data from the study on sandpit play.

Explain three reasons for this choice in the context of this study.

The calculated value of t was 3.576

For this study degrees of freedom (df) = 18

Table 2 Extract from table of critical values of t

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

With reference to the critical values in Table 2 above, explain whether or not there was a significant difference between the two age groups at the 5% level of significance.

Referring to the critical values in Table 2, explain why the researcher is very unlikely to have made a Type I error.

A Wilcoxon test was used to determine whether differences in stress ratings were significant. The psychologist used a 0.01 level of significance.

Explain what it would mean if the results in the above study were significant at the 0.01 level.

The psychologist found that the difference was not significant at the 0.01 level.

The psychologist was concerned that there might have been a type II error.

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

Suggest one way the psychologist could reduce the chance of a type II error.

Suggest an appropriate statistical test that could be used to analyse the data in your study and explain two reasons for your choice in the context of your study.

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.

In an experiment into the effectiveness of the top-down approach to offender profiling, 20 participants were asked to build a profile of an offender using information from real life cases. Half of the participants were given information about a murder case and asked to produce a profile. The other half were given information about a robbery and asked to produce a profile. After the profiling session, each profile was classified as High Accuracy or Low Accuracy.

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.

In an experiment into the effect of reinforcement on gambling, 20 participants played 10 practice card games on a computer. The computer system was pre-programmed so that half of the participants won in games 1, 2, 6, 8 and 10 and the other half won no practice games. After the 10 practice games, each participant played a test game and the amount of money each participant bet in the test game was classified as High Stakes (gambled more money) or Low Stakes (gambled less money).

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 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.

Explain one other reason why the psychologist used a Pearson’s r test in this study.

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

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.

A psychologist investigated the effect of the presence of a friend on mood. She used a controlled laboratory experiment. She asked a group of participants to rate their happiness on a scale.

In Condition 1 (Alone Condition), participants completed the scale after sitting alone in a room for 30 minutes.

In Condition 2 (Friend Condition), the same participants completed the same scale after sitting for 30 minutes in a room with a friend.

The conditions were counterbalanced.

The psychologist analysed the results of the study using a Wilcoxon test. The analysis showed that happiness ratings were significantly higher in the Friend Condition.

Explain two reasons why it was appropriate to use a Wilcoxon test in this situation. Refer to the description of the study in your answer.

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.

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 coefficient for the Spearman’s rho test was 0.395

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 21 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.

When she looks at the results in Table 1, the teacher says, “I can see there is a difference in behaviour between the two conditions, but is the difference significant at the 0.05 level of significance?”

What do the students need to do with the data in Table 1 so that they can answer their teacher’s question? Explain your answer.

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.

In a study of filter theory, a psychology student used a group of female participants. Each participant was shown two descriptions.

• Description 1 described a man with a similar social background to that of the female participants.

• Description 2 described a man with a different social background to that of the female participants.

The student asked participants to judge how much they liked each description on a scale of 1–10.

The student decided to test for a significant difference between the judgements made for each description. He proposed using an unrelated t-test to analyse the data.

Suggest a more appropriate statistical test of difference for the student to use with this data. Explain two reasons for your choice based on the description of the study.

In a study of sex-role stereotypes and the understanding of gender, a psychology student used a group of 7-year-old children. Each child was shown two pictures.

Picture 1 showed people carrying out sex-stereotypical activities.

Picture 2 showed people carrying out non-sex-stereotypical activities.

The student asked the children to say how much they liked each picture on a scale of 1–10.

The student decided to test for a significant difference between the judgements of the two pictures. He proposed using an unrelated t-test to analyse the data.

Suggest a more appropriate statistical test of difference for the student to use with this data. Explain two reasons for your choice based on the description of the study.

In a study of perspective-taking, a psychology student used a group of 9-year-old children. Each child was shown two pictures.

Picture 1 showed an older child being unkind to a little boy.

Picture 2 showed an older child being kind to a little boy.

The student asked the children to judge how sad the little boy would feel in each picture on a scale of 1–10.

The student decided to test for a significant difference between the judgements of the two pictures. He proposed using an unrelated t-test to analyse the data.

Suggest a more appropriate statistical test of difference for the student to use with this data. Explain two reasons for your choice based on the description of the study.

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.

The results of the study are given in Table 2, below.

The researcher decided to use the Sign Test to see whether there was a significant difference in the improvement in the scores between the two groups at the 5% level of significance.

Calculate the value of S in this study. Show your workings.

Table 3 Table of critical values of the sign test (S)

Significance is shown if the calculated value of S is equal to or less than the critical value.

Explain whether or not there was a significant difference in the improvement in the scores between the two groups. Use your answer to Question 22 and Table 3.

A psychology teacher read the 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.

In a study of communication, researchers used a language rating scale to compare two groups of participants. Participants in Group A were a volunteer sample of people from a self-help group for people with schizophrenia. Participants in Group B, the control group, were a volunteer sample of people who attended a community centre.

The researchers used an inferential statistical test to see if there was a significant difference in language rating between the two groups.

Explain why a Mann-Whitney test is an appropriate choice of statistical test in this situation and a Spearman’s test is not.

In a study of body image, researchers used a body image rating scale to compare two groups of participants. Participants in Group A were a volunteer sample of people who attended a self-help group for people with eating disorders. Participants in Group B, the control group, were a volunteer sample of people who attended a community centre.

The researchers used an inferential statistical test to see if there was a significant difference in body image rating between the two groups.

Explain why a Mann-Whitney test is an appropriate choice of statistical test in this situation and a Spearman’s test is not.

In a study of stress, researchers used a stress rating scale to compare two groups of participants. Participants in Group A were a volunteer sample of people who attended a self-help group for people with stress. Participants in Group B, the control group, were a volunteer sample of people who attended a community centre.

The researchers used an inferential statistical test to see if there was a significant difference in stress rating between the two groups.

Explain why a Mann-Whitney test is an appropriate choice of statistical test in this situation and a Spearman’s test is not.

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

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

The psychologist found that the difference in the number of nightmares reported in the two conditions was significant at p<0.05.

Explain what is meant by ‘significant at p<0.05’ in the context of this experiment.

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 on page 2 is 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.

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 2 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 2, explain whether or not the results are significant.

What is meant by a Type II error? Explain why psychologists normally use the 5% level of significance in their research.