SPSS data analysis of numeric variables and their relationships

SPSS Data Analysis

Does the number of average study hours per week during the semester accurately predict final exam grades?

Independent variable: average number of study hours per week.

Hours is continuous data because it can take on any value below 168 hours, which is the number of hours in a week. Even though the data is reported in integer form the 'hours' data is continuous.

Hours data is quantitative, since it can be summed, divided, and multiplied.

Hours data is ratio data because it has a natural zero point. For example, the range of hours that a student can theoretically study per week is between zero and 168 hours.

Hours is a predictor variable, because it is believed/assumed to influence the outcome of the study.

Dependent variable: Final exam score.

Final exam scores is a discrete variable as reported, although it could be a continuous variable with a value anywhere between zero and 100.

Exam scores are quantitative, because it can be added, divided and multiplied.

iii. Exam scores is ratio data because it has a natural zero point.

iv. Since exam scores is the outcome variable, it is also the criterion variable for statistical tests like linear regression.

Descriptive Statistics

The total number of students who took part in the study were N = 20, with none dropping out during the semester. The overall average of hours studied per week was M = 12.25, but the middle and most common values were Mdn = 11.00 and Mode = 10, respectively. The minimum and maximum average of hours studied per week was 4 and 22 hours, respectively, so the measures of central tendency suggest most students were clumped at middle of the frequency distribution.

The frequency distribution had a Range = 18, with a minimum and maximum average of 4 and 22 hours, respectively. The average dispersion around the mean was SD = 5.389. Together, the range and standard deviation reveal a wide frequency distribution around the mean and considerable variability in the average number of hours studied per week. With a skewness value of 0.177 the frequency distribution is shifted slightly in favor of lower hours studied per week by most students, but there were a few overachievers that averaged a high number of hours per week.

Correlation

A good way to view possible relationships between the independent and dependent variable is the scatterplot. When average hours studied per week is plotted against final exam scores using a scatterplot it becomes apparent that there is a linear and positive relationship. However, to determine the strength of this relationship a Pearson's product-moment correlation coefficient (r) can be calculated for these two variables. Based on the SPSS results, there is a very strong, statistically significant correlation between hours and scores [r (18) = .967, p < .01, two-tailed]. The percentage of the variation in the dependent variable due to the independent variable is also very high (r2 = .934), which suggests that the average number of hours per week studied may be responsible for 93.4% of the final exam grade; however, a correlation cannot determine causality, only that there is a strong association between the two variables.

There are a number of potential ethical considerations concerning how the data was collected in this study. Of primary concern was the possibility that average hours studied could influence final grades for the course, but the professor collected this data at the end of the semester during the final examination. While there is still a potential ethical concern, the assumption is that the final exam was graded before the data was viewed and analyzed. Even so, most students would expect the hours data and final exam scores to remain confidential during the grading period.

Regression