Research Methods- Tests of correlation: Spearman's and Pearson's Flashcards
Why Spearman’s rho?
Spearman’s rho is a test of correlation between two sets of values. It is selected when one or both variables are ordinal level (though it can also be used with interval data). The design is correlational rather than experimental.
What is the level of measurement in this example?
The level of measurement is ordinal, as the data is based on subjective ratings of attractiveness, which are converted to ranks for the test.
What is the aim of the study?
The study investigates the matching hypothesis, which proposes that couples in long-term relationships tend to be similar in physical attractiveness. Twelve couples were selected, and their photographs were rated by 20 participants for attractiveness on a scale of 1-20. The median attractiveness rating for each photograph was calculated to determine if there was a correlation between partners.
What is the alternative hypothesis?
The alternative hypothesis is that there is a positive correlation between ratings of physical attractiveness given to two partners in a relationship. (directional, one-tailed)
What is the null hypothesis?
The null hypothesis is that there is no correlation between ratings of physical attractiveness given to two partners in a relationship.
What is Step 1 in the Spearman’s rho analysis?
Step 1 involves ranking each set of scores separately (for each partner in the couple) from lowest to highest. If scores share the same ranks, the mean of their total ranks is assigned.
What is Step 2 in the Spearman’s rho analysis?
Step 2 involves calculating the difference between each pair of ranks, squaring the differences, and summing the squared differences (Σd²).
What is Step 3 in the Spearman’s rho analysis?
Step 3 involves calculating the value of rho using the formula:
[ \text{rho} = 1 - \frac{6 \Sigma d²}{N(N² - 1)} ]
In this example, ( \text{rho} = 1 - \frac{6 \times 296}{12(144 - 1)} = -.035 ).
What is Step 4 in the Spearman’s rho analysis?
Step 4 involves comparing the calculated value of rho (-.035) to the critical value of rho (.503) for a one-tailed test at the 0.05 level where N = 12. Since the calculated value (ignoring the sign) is less than the critical value, the result is not significant (p ≤ 0.05).
What conclusion is drawn from the Spearman’s rho analysis?
The null hypothesis is accepted: There is no correlation between ratings of physical attractiveness given to two partners in a relationship (p ≤ 0.05). Additionally, the result is in the wrong direction (negative rather than positive), so the hypothesis would not be accepted even if the calculated value was sufficiently large.
Why Pearson’s r?
Pearson’s r is a test of correlation between two sets of values. It is selected when the data are interval level. The design is correlational rather than experimental.
What is the level of measurement in this example?
The level of measurement is interval, as the data is based on ‘safe’ mathematical scales (public measurement).
What is the aim of the study?
The study investigates whether there is a relationship between the length of time (in days) spent using biofeedback and the reduction in resting heart rate (measured in beats per minute, bpm). Ten participants experiencing chronic stress were selected, and their baseline heart rate (before biofeedback) was compared to their current heart rate to calculate the reduction.
What is the alternative hypothesis?
The alternative hypothesis is that there is a positive correlation between the number of days participants have been using biofeedback and the reduction in their resting heart rate. (directional, one-tailed)
What is the null hypothesis?
The null hypothesis is that there is no correlation between the number of days participants have been using biofeedback and the reduction in their resting heart rate.
What is Step 1 in the Pearson’s r analysis?
Step 1 involves creating a table of data and calculating the following:
- The sum of the scores for x (Σx) and y (Σy).
- The square of each x value (x²) and each y value (y²).
- The product of x and y for each participant, summed as Σ(xy).
What is Step 2 in the Pearson’s r analysis?
Step 2 involves calculating the value of r using the formula:
[ r = \frac{N(\Sigma xy) - (\Sigma x)(\Sigma y)}{\sqrt{[N \Sigma x² - (\Sigma x)²][N \Sigma y² - (\Sigma y)²]}} ]
In this example, ( r = \frac{10(2059) - (340)(49)}{\sqrt{(171080 - 115600)(2910 - 2401)}} = .740 ).
What is Step 3 in the Pearson’s r analysis?
Step 3 involves comparing the calculated value of r (.740) to the critical value of r (.549) for a one-tailed test at the 0.05 level where degrees of freedom (df) = N - 2 = 8. Since the calculated value is greater than the critical value, the result is significant (p ≤ 0.05).
What conclusion is drawn from the Pearson’s r analysis?
The null hypothesis is rejected, and the alternative hypothesis is accepted: There is a positive correlation between the number of days participants have been using biofeedback and the reduction in their resting heart rate (p ≤ 0.05).
