A human factors psychologist is interested in the role that spatial ability has on pilot performance. She records the scores of 5 pilot's spatial ability (0-10 scale) and then counts the number of errors they make in experimental pilot task designed to be very difficult. Previous research has shown that there is a relationship between spatial ability and pilot performance. N = 5, M_x = 6.8, M_y = 11.6

Sketch a scatterplot of these data.

Find SSx:

Find SSy:

Find SSxy

What is your calculated r value?

Is this a strong correlation? Weak? Moderate?

Check in SPSS

Next, conduct a hypothesis test (alpha = .05) on the correlation between the two variables, where the null hypothesis is no relationship between spatial ability and the number of errors made.

State the prediction as a set of hypotheses.

Identify the test statistic and the test distribution.

Determine the critical value on the test distribution.

Compute the test statistic.

Decide whether to reject the null hypothesis, and report the r-statistic with its degrees of freedom and p-value (i.e., p less than or greater than alpha).

Compute the effect size, and interpret it using the words of the problem.

Regression

Find the slope (b₁) of the regression line for spatial ability (X) predicting the number of errors made (Y).

Interpret the slope as a change in the number of errors made per unit change in spatial ability.

Find the intercept (b₀) of the regression line.

Write the regression equation.