Study hours as a predictor of final exam grades

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.

Regression

The predictor variable (Y) is the dependent variable, which in this study were the final exam scores. The criterion variable (X) is the independent variable, or in this case the average hours of study per week. The form of the basic linear regression equation is Y = ?0 + ?1X1 + ?2X2 + & #8230; nXn + ?n, with ?0 representing the Y-intercept, ?1-n representing the slope, and ?n representing the errors of prediction. The values of the dependent variable can therefore be estimated by the regression equation: Y = 47.918 + 2.619*X, with ?1-n = 2.619, t (18) = 16.014, p < .0001. For example, if a student wanted to know what grade they might get if they studied 15 hours a week then he or she would substitute 15 hrs for X in this equation and get a predicted final exam score of 87. The accuracy of this prediction depends on the amount of variation in the data, which is the difference between the best fit line and the experimental values (Y -- Y' = ?) and is given as the standard error of the estimate (SEE = 3.842). These calculations allow students and professors to predict how much studying must occur on a weekly basis to get a desired final exam grade; however, linear regression cannot determine the direction of causality, only the predictive strength of the independent variable. Causality is assumed given the respective nature of the two variables. The ethical concerns for data collection are the same as discussed above for correlation.