Psy 429 Experimental Psychology
Class Exercise #1
Statistical Notation, Descriptive Statistics, and Correlation
Answers
Psy 429 Experimental Psychology
Class Exercise #1
Statistical Notation, Descriptive Statistics, and Correlation
Answers
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 a sample of 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.'
Individual X
[frequency] x2 Y
[importance] Y2 XY 1 4
16 5 25 20 2 1 1 7 49 7 3 2 4 3 9 6 4 8 64 2 4 16 5 8 64 1 1 8 6 2 4 1 1 2 7 5 25 4 16 20 8 7 49 7 49 49
Perform the following calculations:
a. S X = 37b. S Y = 30
c. S XY = 128
d. (S X)/N = 4.625
e. (S Y)/N = 3.75
f. S X2 = 227
g. S Y2 = 154
h. (S X)2 = 1369
i. (S Y)2 = 900
2. What is the notation for the following:
a. mean of the population: mb. standard deviation of the population: s
c. mean of a sample: M or X with a line over it
d. standard deviation of a sample: s
e. variance of the population: s2
f. variance of a sample: s2
3. Calculate the sum of squares (SS), variance, standard deviation, and mean of the data in question 1 above.
For variable X: M = 4.63, SS = 55.87, s2 = 7.98, and s = 2.83For variable Y: M = 3.75, SS = 41.5, s2 = 5.93, and s = 2.43
4. Calculate the correlation coefficient (r) for the data in question 1 above.
r = - .22
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.
Eight participants were asked to respond to two questions, one asking about their frequency of attending worship services and the other asking about the importance of religion or spirituality in their lives. Each question was scaled on a 10-point Likert-type scale in which 1 = "not at all" for the frequency question, or "not important at all" for the importance question, and 10 = "every chance I get" or "extremely important." The mean score for the frequency question was 4.63 with a standard deviation of 2.83 and the mean score for the importance question was 3.75 with a standard deviation of 2.43.To determine whether there was a relationship between frequency of attending worship services and the importance of religion or spirituality in their lives, a Pearson r correlation coefficient was calculated. A scatterplot reflected a linear relationship with a correlation coefficient of - .22, indicating that for these eight individuals, the more they attended worship services, the less likely they were to report that religion or spirituality was important in their lives.
6. What information is conveyed by the 'magnitude' of a correlation coefficient?
The strength of the relationship between the two variables. The closer the value is to + or - 1.00, the more the two variables are related.
7. What information is conveyed by the 'sign' of a correlation coefficient?
The direction of the relationship. A positive (+) sign indicates a positive correlation- as one variable increases so does the other (or as one goes down, so does the other) ; a negative (-) sign reflects a negative correlation - as one variable goes up the other goes down, and vice versa.
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?
- linear relationship between the two variables, X and Y
- homoscedasticity
- variables normally distributed
- random sampling of X and Y
10. Define a partial correlation and give an example using the two variables in question 1 above.
Partial correlation is when a third variable is partialled out or kept constant (controlled) from both variables, X and Y.An example is when a researcher wants to determine whether a relationship exists between frequency of attending worship services and the reported importance of religion or spirituality but wants to control for level of stress currently experienced.
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