Research Methods Statistics in Psychology

Question

Research Scenario: Is there a positive relationship between grit and GPA in high school seniors? A researcher examined this issue by having students beginning their senior year of high school complete a grit inventory using a Likert-based scale (range 1 – 7), where higher numbers indicate more “grit”. GPA was self-reported (scale 0 – 4.0). Enter the data shown here into SPSS to assess whether there is a positive relationship between grit and GPA.

Grit	GPA
6.5	4.0
4.0	3.1
3.7	2.7
5.8	3.5
4.7	3.1
5.5	3.3
3.9	2.7
1.1	2.8
3.5	3.1
2.7	2.6
5.1	3.8
3.2	2.2
5.6	2.8
6.1	2.5

Answer 1

At the most basic level, you're likely expected to determine a correlation coefficient, measuring the relationship between these two metrics (grit and GPA). A more complete analysis would include running a linear regression to test the hypothesis that the presumed dependent variable, GPA, is influenced by the independent variable, grit. If you were to take things just one step further, there are a number of statistical analyses you might use to explore the relationship between grit and GPA in greater depth.

To check your work in SPSS, here are the critical results that you should get:

1) The correlation.

correlation = 0.5226

Note that this correlation is not particularly tight--a 'perfect' correlation would be 1.0. This was calculated using R and the script shown below, where 'data' is a data frame containing the grit and GPA data.

cor(data$Grit, data$GPA)

2) A linear regression model of the data,

model <- lm(GPA ~ Grit, data = data)

shows that

summary(model)

there's marginal support at best for the hypothesis that grit determines GPA:

Adjusted R-squared = 0.2126, F(1, 12) = 4.51, p = 0.05518

Note that the adj R-squared provides an estimate of variance explained, and the p-value gives the probability that the slope of the line is greater than 0 (ie that the dependent variable is in fact dependent on the independent variable). So, while there is a positive correlation, it's a weak one at best.

3) However, your data do not look particularly linear.

scatter.smooth(x=data$Grit, y=data$GPA)

Run this and you'll get a figure that suggests a non-linear relationship--if there even is one! These are warning signs that a linear model may not be appropriate, but that is probably beyond the scope of your question.

I realize that you're expected to use SPSS, but the premise is the same whatever software you use for the analysis. Use these results to check your work in SPSS. I've imported the data into R as a data frame ('data'). Let me know if there's anything you don't understand...or if you'd like help using R!

Note that the adj R-squared provides an estimate of variance explained, and the p-value gives the probability that the slope of the line is greater than 0 (ie that the dependent variable is in fact dependent on the independent variable). So, while there is a positive correlation, it's a weak one at best.

Answer 2

I didn't use SPSS, I used a TI-84 calculator, entered the data in and performed a linear regression analysis. It showed an r value of 0.52, which is positive correlation, but it isn't very strong. Closer to 1 would be better.