PSY 429 Experimental Psychology

Class Exercise #1

Statistical Notation, Descriptive Statistics, and Correlation

 

1. Supposing a researcher was interested in getting information on the frequency of individuals' religious or spiritual attendance at worship services and how important religion or spirituality is in their lives. The researcher constructed several questions related to these two questions and asked eight individuals to respond. Consider the following data below. The variable 'X' reflects the score on the question about religious attendance with the higher number reflecting more frequent attendance and the lower number less frequent attendance (on a scale from 1 to 10). The variable 'Y' reflects importance of religion or spirituality in the individual's life, on a scale of from 1 to 10, with 1 being 'not important at all' to 10 being 'extremely important.'

Perform the following calculations:

a. S X =

b. S Y =

c. S XY =

d. (S X)/N =

e. (S Y)/N =

f. S X² =

g. S Y² =

h. (S X)² =

i. (S Y)² =

2. What is the notation for the following:

a. mean of the population

b. standard deviation of the population

c. mean of a sample

d. standard deviation of a sample

e. variance of the population

f. variance of a sample

3. Calculate the sum of squares (SS), variance, standard deviation, and mean of the data in question 1 above.

4. Calculate the correlation coefficient (r) for the data in question 1 above.

5. State in words the results of the descriptive statistics and what the relationship is for these eight individuals between frequency of attendance at worship services and importance of religion/spirituality.

6. What information is conveyed by the 'magnitude' of a correlation coefficient?

7. What information is conveyed by the 'sign' of a correlation coefficient?

8. Draw a hypothetical scatterplot of two variables, for example, GPA and SAT scores, in which the relationship reveals a LACK of homoscedasticity.

a. Based on your graph, for high GPA scores, will the overall correlation coefficient be underestimated or overestimated?

b. Based on your graph, for low GPA scores, will the overall correlation coefficient be underestimated or overestimated?

 

9. What are the assumptions and requirements underlying the Pearson r correlation coefficient?

10. Define a partial correlation and give an example using the two variables in question 1 above.

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