Chi-Square, T-Test and Correlation Research Methods in Psychology a (HPS201/HPS771)

Crosstabs and Chi-Square

Scenario

Some researchers have suggested that there are two main types of personality: Type A and Type B. Individuals with Type A personality are characterized as being conscientious and competitive. They strongly desire success and typically present with higher levels of stress. Conversely, individuals with Type B personality are typically less stressed and tend to be more laconic, relaxed and less concerned with competition.

Due to the higher levels of stress experienced by those with Type A personality, health insurance risk evaluators are interested in knowing whether individuals with Type A personality are at greater risk of having a heart attack.

You are hired as a researcher to investigate this research question. You take a random sample of 40 individuals aged between 40 and 60 years and assess their personality to determine whether they possess a Type A or Type B personality. You then ask them whether they have experienced a heart attack before (yes/no). You then run a Chi-Square test of independence to determine whether there is a relationship between Personality Type (A or B) and Heart Attack incidence (Yes or No) and obtain the following data:

Personality Type * Heart Attack Incidence Crosstabulation

Heart Attack Incidence

Total

Yes

No

Personality Type

Type A Personality

Count

15

8

23

Expected Count

10.9

12.1

23.0

Type B Personality

Count

4

13

17

Expected Count

8.1

8.9

17.0

Total

Count

19

21

40

Expected Count

19.0

21.0

40.0

Value

df

Asymp. Sig. (2-sided)

Pearson Chi-Square

6.812a

1

.009

Continuity Correctionb

5.243

1

.022

Likelihood Ratio

7.081

1

.008

Fisher's Exact Test

Linear-by-Linear Association

6.642

1

.010

N of Valid Cases

40

a. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 8.08.

b. Computed only for a 2x2 table

Questions

1. Under what experimental conditions would it be appropriate to run a chi-square test of independence?

A chi-square test for independence would be used when there are two categorical variable for one group (or population. It is used to assess if there is a single association between two variables. For example, if there was an election survey occurring there might be information gathered based on gender or political party affiliation: thus a chi-square test can be useful to determine how these factors relate to voting preference.

/2 Marks

2. Complete the following chi-square table. Insert both the observed and expected frequencies (expected frequencies should appear in parentheses).

Heart Attack

No Heart Attack

Type A

____4

Type B

/1 mark

.5 mark correctly entering observed values

.5 mark correctly entering expected values

3. Is personality type associated with heart attack incidence? If so, describe the relationship? Use appropriate statistics to support your answer.

Based on the data, personality type is indeed associated with occurrence of heart attacks. This is something which has long been known to researchers. For example, Friedman and Rosenman are two cardiologists that discovered that "people with type A personality run a higher risk of heart disease and high blood pressure than type Bs. Their theory was based on an observation of the patients with heart conditions in their waiting room. Unlike most patients, who wait patiently, some people seemed unable to sit in their seats for long and wore out the chairs. They tended to sit on the edge of the seat and leaped up frequently" (McLeod, 2011).

/ 2 marks

1 mark for correct answer

1 mark for correctly describing the relationship between the variables

4. With help from your text book and the previous example, report the results of the analysis in APA format including all relevant information

The reality is that the work of Friedman and Rosenman have long demonstrated the strong correlation between personality type and heart attacks. When gathering research on the matter, they asked subjects question to the effect of: do you feel guilty when you take time to relax? Or do you need to win when playing games or sports? Do you generally move, talk, and eat quickly?

Within eight years, "257 of the participants had developed coronary heart disease. By the end of the study 70% of the men who had developed coronary heart disease (CHD) were type A personalities" (McLeod, 2011). This meant that the behavior type A personality was more likely to manifest illnesses connect to stress, elevated blood pressure (McLeod, 2011).

/ 5 marks

TOTAL: / 10 Marks

Research Methods in Psychology...

As a Developmental Psychologist, you conduct an experiment to test this theory. You take a sample of 30-17-year-olds who grew up and continue to live in 'rural' Victoria, and another 30- to 17-year-olds who grew-up and continue to live in 'metropolitan' Victoria. You then assess each participant's motor ability using a standardized test of motor skill [M=100, SD=15)].
You run an independent samples t-test to determine whether the mean motor ability of 'rural' children is different from the mean motor ability of 'metropolitan' children. Based-on previous research, you would predict that the 'rural' group would have better motor skills than the 'metropolitan' group. You obtain the following data:

The first two questions do not require you to use the above output.

1. Under what experimental conditions would it be appropriate to conduct a single-sampled t-test? In such a scenario, why would a researcher adopt a single-sampled t-test rather than a z-test?

Researchers generally harness the one-sample t-test when individuals want to determine whether our sample is derived from certain populations, but there are no complete populations available. One example would be if one wanted to know if a certain group of college students resembles or is distinct from college students overall: thus, the one sample t-test is connected only for tests with a sample mean (emory.edu).

/ 2 Marks

2. A researcher wishes to determine whether the mean depression rating of a group of elderly men changes after they have undergone a mental health workshop. Each participant completes the Beck Depression Inventory (scores range from 0 to 63) before and after the workshop. What kind of t-test should the researcher use to compare the mean depression rating of participants before and after the workshop? Given that there are 3 types of t -- test, what makes the other two types of t-test inappropriate for this scenario?

The one sample t-test would be ideal for this scenario, just because it involves one sample -- one group. The other two types of t-tests would generally be inappropriate for this scenario because of the fact that they involve comparisons between two groups.

/ 2 Marks

The remaining questions relate to the above SPSS output.

3. Has the assumption of homogeneity of variance been met or violated? Use statistical information to support your answer.

It appears that based on the data displayed and the different results found, the homogeneity of variance has indeed been violated -- as the results demonstrate no homogeneity.

/ 2 marks

1 mark for correct answer

1 mark for correct use of statistics

4. Based on a visual inspection (this means, just by looking at the data) of the group means and standard deviations, do you anticipate that there will be a significant difference between the mean motor abilities of the 'rural' and 'metropolitan' groups? Justify your answer.

/1 mark

There is not a reasonable basis to expect a significant difference between mean motor abilities of the rural and metropolitan groups: the visual inspection demonstrates very little distinction between the data sets.

5. How would you interpret the results of this analysis? Write a short paragraph in APA format describing this analysis including all relevant information.

/ 3 marks

Based on an analysis of the data, there isn't a significant difference between the motor abilities of children from rural areas vs. from metropolitan areas. This demonstrates that things like population size and environment don't have a significant impact on how children develop motor skills. It also implies that things like variety and type of stimulation don't have a strong impact on how children develop motor skills, as well as implies that sound, noise and pollution have equally insignificant impacts on this arena of a child's development.

Total

/10 Marks

Research Methods in Psychology A (HPS201/HPS771)

Assignment 1.3

Correlation

Experiment

You are hired as an Industrial Psychologist by a local Coffee shop to investigate the factors that influence how much coffee is being sold during a day. You believe that the daily temperature may be associated with coffee sales. Accordingly, you visit the coffee store on 35 occasions throughout the year. Each time you record the number of coffees that were sold during that day, as well as the daily temperature high.

You run a Pearson's correlational analysis on the data to investigate the relationship between daily coffee sales and daily temperature high. The data are as follows:

The first two questions do not require you to use the above output.

1. Explain how a correlational analysis is similar to a Chi-square test of independence.

Correlational analysis is comparable to a chi-square test of independence in that they both are examining a sense of relationship, and the strength of that relationship between two factors. With something like correlational analysis, a high correlation means that there's a strong relationship, and a low correlation likewise signifies a weak relationship. In a similar fashion, the chi-square test is used when one is engaging with two nominal variables.

/1 mark

2. Explain when a correlational analysis would be used rather than a Chi-square test of independence.

A Chi -- square test of independence would be used when its…