Statistical Analysis Sample: Correlation Analysis of Study Hours and Academic Grades

Model Answer

Introduction and Research Question

The relationship between how much time students spend studying and the grades they subsequently achieve is one of the most frequently investigated questions in educational and study-skills research, yet findings on the strength of this relationship vary considerably across studies and student populations (Credé and Kuncel, 2008). This report presents a Pearson product-moment correlation analysis conducted to establish whether, and how strongly, weekly study hours are associated with final examination grade among a sample of undergraduate students.

The analysis was undertaken as part of a first-year research methods module, using data collected from a voluntary self-report survey distributed to students following the release of their examination results. Because both variables of interest — weekly study hours and examination grade — are continuous, interval-level measures, a Pearson correlation coefficient was the appropriate statistic for quantifying the strength and direction of their linear relationship (Field, 2018), rather than a test suited to categorical data such as chi-square, or a test comparing group means such as a t-test.

The research question was: is there a statistically significant linear relationship between the number of hours a student reports studying per week and their final examination grade, and if so, how strong is that relationship? The null hypothesis (H0) stated that the population correlation between study hours and examination grade is zero (ρ = 0), meaning no linear relationship exists. The alternative hypothesis (H1) stated that the population correlation is not equal to zero (ρ ≠ 0), meaning a linear relationship does exist. A two-tailed test was used throughout, since the analysis did not assume in advance that any relationship, if present, would necessarily be positive, even though a positive relationship was the more plausible outcome on theoretical grounds. The following sections describe the sample and variables, the assumption checks undertaken, a worked illustration of the correlation calculation, the full-sample test output, and a plain-English interpretation of the findings.

Data and Variables

Data were collected from 60 undergraduate students (N = 60) enrolled on a range of degree programmes at a UK university, via an anonymous online questionnaire administered shortly after examination results were released. Participants were recruited through a departmental email invitation and a short social media post, with a small prize draw offered as an incentive to encourage participation. Weekly study hours were self-reported in response to the question “On average, how many hours per week did you spend studying for this module, outside of timetabled classes?” and were recorded as a whole number. Final examination grade was recorded as the percentage mark awarded for the module examination, as reported by the student from their official results.

The module in question was a Level 4 introductory statistics module taken by students from several allied health and social science honours degrees, chosen for this analysis precisely because study time is often assumed, rather than empirically demonstrated, to matter for performance on quantitative modules of this kind. Response accuracy for the self-reported examination grade was cross-checked against the module’s anonymised grade distribution supplied by the department, and no implausible values (for example, grades outside the 0–100% range) were identified.

Both variables were treated as continuous for the purposes of the analysis. Because study hours were self-reported rather than objectively logged — for example, via a study-tracking application or timetable records — some degree of measurement error is likely, a point returned to in the Limitations section below. Table 1 presents the descriptive statistics for both variables across the full sample.

Study hours ranged from 3 to 25 per week (M = 12.4, SD = 4.8), while examination grades ranged from 38% to 92% (M = 64.2, SD = 11.6). Both variables showed a reasonable spread typical of an undergraduate cohort, with no evidence of severe restriction of range at either the top or bottom of the scale that would be likely to artificially suppress the resulting correlation coefficient.

Preliminary Checks and Assumptions

Four assumptions were checked before interpreting the Pearson correlation, following standard guidance for parametric bivariate analysis (Field, 2018; Pallant, 2020).

First, both variables were required to be continuous or interval-level, which was satisfied: study hours and examination percentage are both measured on genuinely continuous scales rather than as ranked or categorical data, which is what justified the choice of Pearson’s r over a non-parametric alternative such as Spearman’s rho.

Second, the relationship between the two variables was checked for linearity by inspecting a scatterplot (Figure 1, below). The plotted points showed a reasonably linear upward pattern with no obvious curvature, which is a necessary condition for a Pearson correlation to be an appropriate summary of the relationship; a strongly curvilinear pattern would have understated the true strength of association if left unaddressed.

Third, both variables were checked for approximate normality using the Shapiro-Wilk test and a visual inspection of Q-Q plots, since Pearson’s r assumes each variable is approximately normally distributed for the associated significance test to be fully valid in smaller samples. Study hours did not differ significantly from a normal distribution, W = 0.978, df = 60, p = .361, nor did examination grade, W = 0.971, df = 60, p = .163. Both results were non-significant, meaning the null hypothesis of normality could not be rejected for either variable at conventional significance levels.

Fourth, the data were screened for univariate and bivariate outliers using boxplots and standardised z-scores; no case exceeded ±3.29 standard deviations from the mean on either variable, and no case appeared as a clear bivariate outlier when inspecting the scatterplot. On this basis, all 60 cases were retained, and homoscedasticity — an even spread of points across the range of the scatterplot, rather than a fan or cone shape — was also visually confirmed. With all four assumptions reasonably satisfied, the Pearson correlation could be interpreted with confidence.

Test Results

To illustrate how the Pearson correlation coefficient is calculated by hand, Table 2 works through the procedure using a simplified illustrative subsample of eight students drawn from the dataset, before the full-sample SPSS result is reported. The formula for Pearson’s r is:

r = Σ(x − x̄)(y − ȳ) / √[Σ(x − x̄)² × Σ(y − ȳ)²]

For this illustrative subsample, the mean study hours was x̄ = 12.13 and the mean grade was ȳ = 65.38. Summing the final three columns of Table 2 gives Σ(dx·dy) = 502.63, Σdx² = 236.87 and Σdy² = 1413.87. Applying the formula: r = 502.63 / √(236.87 × 1413.87) = 502.63 / 578.72 = .87. This confirms, on a small hand-calculated subsample, a strong positive relationship between study hours and grade — a useful sense-check that the direction and rough magnitude of the relationship make intuitive sense before turning to the full dataset. A subsample of eight is, of course, too small to draw any reliable conclusion on its own, and its coefficient is not expected to exactly match the full-sample figure.

For the complete sample (N = 60), the same calculation was performed in SPSS (version 28) across all 60 cases, returning a Pearson correlation coefficient of r = .58. Table 3 reports the full SPSS-style correlation output.

SPSS reports the exact significance value as .000 to three decimal places; following APA convention, this is written as p < .001 rather than p = .000, since a probability can never be exactly zero. The coefficient of determination was calculated as r² = .3364, indicating that approximately 33.6% of the variance in examination grade can be statistically accounted for by weekly study hours. A 95% confidence interval for the population correlation was calculated using Fisher’s r-to-z transformation, giving a lower bound of .38 and an upper bound of .73.

Because a bivariate Pearson correlation between two continuous variables is mathematically equivalent to a simple linear regression with one predictor, the same relationship was also expressed in regression form for completeness, using the standard formulae b = r × (SD_y / SD_x) and a = ȳ − b × x̄. Table 4 reports the resulting coefficients.

The unstandardised slope (b = 1.40) indicates that, on average, each additional hour of weekly study was associated with a 1.40 percentage-point increase in examination grade. The standardised coefficient (β = .58) reported here is identical to the Pearson r reported above, and the associated t-value (t = 5.38) closely matches the correlation significance test (t = 5.42, allowing for rounding in the intermediate B and SE values), confirming that the correlation and simple regression framings are two equivalent ways of describing the same underlying linear relationship.

Figure 1 displays the full-sample scatterplot with a fitted trend line, illustrating the positive linear relationship underlying the reported correlation.

Interpretation

The Pearson correlation between weekly study hours and examination grade was positive, moderate-to-strong, and statistically significant, r(58) = .58, p < .001, 95% CI [.38, .73]. Using Cohen’s (1988) benchmarks for correlation coefficients (small = .10, medium = .30, large = .50), this result falls in the large-effect range, indicating a relationship that is not only statistically reliable but also substantively meaningful for this cohort.

In plain terms, students who reported studying more hours per week tended to achieve considerably higher examination grades, and this pattern is highly unlikely to have arisen by chance (p < .001). The coefficient of determination (r² = .336) indicates that just over a third of the variation in examination grades across this cohort can be statistically linked to differences in reported weekly study hours, leaving the remaining two-thirds of variation attributable to other factors not captured in this analysis — such as prior attainment, the quality rather than the quantity of study undertaken, class attendance, or individual differences in learning ability and prior subject knowledge.

It is important to stress, in line with standard good practice in reporting correlational findings, that this result establishes association rather than causation (Howitt and Cramer, 2020). While it is plausible that studying more causes higher grades, it is equally plausible that students who are already performing well are more motivated to study, or that a third variable — such as underlying academic ability, interest in the subject, or effective time-management skills — drives both study hours and grades simultaneously. The cross-sectional, correlational design used here cannot distinguish between these competing explanations.

The wide confidence interval (.38 to .73) also deserves comment: while the point estimate of r = .58 suggests a fairly strong relationship, the true population correlation could plausibly be considerably weaker (.38, still a moderate effect) or considerably stronger (.73, a very large effect) than the sample estimate suggests. This reflects the relatively modest sample size (N = 60) and is a useful reminder that a single point estimate should always be interpreted alongside its interval, rather than in isolation. It is also worth noting that the observed correlation is somewhat higher than the average effect sizes reported in some of the wider study-habits literature, where correlations between self-reported study behaviour and academic performance are more commonly in the .20 to .40 range once a broader range of study-skill variables is considered (Credé and Kuncel, 2008); this may reflect genuine cohort-specific factors, or it may partly reflect shared self-report bias, since students who over-report their study hours may also be inclined to recall or round their grades more favourably (Paulhus, 1991).

For practical purposes, these findings offer reasonable support for study-skills interventions that encourage students to increase time spent studying, while cautioning that study hours alone explain only a partial share of grade variation, and that quality of study, prior attainment and other factors are also likely to matter a great deal.

The simple regression framing reported above also gives a concrete, easily communicated figure for feeding back to students and academic support staff: on average, each additional hour of weekly study was associated with a 1.40 percentage-point increase in examination grade, holding the general caveats about causation firmly in mind. Presented this way, a student currently studying five hours a week might reasonably be advised that, all else being equal, doubling their study time to ten hours a week is associated with an average grade increase in the region of seven percentage points — a tangible, motivating figure, provided it is communicated alongside the important caveat that this is an average association observed in one cohort, and individual students may see a considerably larger or smaller benefit, or none at all.

Conclusion and Limitations

This analysis found a statistically significant, moderate-to-strong positive correlation between weekly study hours and examination grade among a sample of 60 UK undergraduate students, r(58) = .58, p < .001, 95% CI [.38, .73], with study hours statistically accounting for approximately 33.6% of the variance in grade.

Several limitations should be considered. First, and most importantly, correlation does not establish causation; the direction of the relationship, and the possible role of confounding variables such as prior academic ability or motivation, cannot be determined from this design alone. Second, study hours were self-reported rather than objectively measured, for example via a study-log or learning-platform time-tracking data, which may have introduced recall or social-desirability bias and could have inflated or attenuated the true relationship (Paulhus, 1991). Third, the sample was drawn from a single university and a relatively modest sample size (N = 60), which limits both the statistical precision of the estimate, reflected in the fairly wide confidence interval, and the generalisability of the findings to other institutions or student populations. Fourth, “study hours” was treated as a single undifferentiated quantity, without distinguishing between more and less effective study strategies, which prior research suggests may matter as much as, or more than, raw time spent (Credé and Kuncel, 2008). Fifth, the sample was recruited voluntarily and incentivised with a prize draw, which may have attracted a subset of students who differ systematically, in either motivation or academic performance, from the wider student population who chose not to take part.

Future research could usefully address these limitations by using objective measures of study time, incorporating measures of study quality and strategy alongside quantity, and replicating the analysis across a larger, multi-institution sample to narrow the confidence interval around the population correlation. Notwithstanding these limitations, the present findings offer reasonable evidence that study time is meaningfully, if imperfectly, related to examination performance in this cohort, providing a useful starting point for further research or for informing the study-skills guidance offered to students.

References

Cohen, J. (1988) Statistical Power Analysis for the Behavioral Sciences. 2nd edn. Hillsdale, NJ: Lawrence Erlbaum.

Credé, M. and Kuncel, N.R. (2008) ‘Study habits, skills, and attitudes: the third pillar supporting collegiate academic performance’, Perspectives on Psychological Science, 3(6), pp. 425–453.

Field, A. (2018) Discovering Statistics Using IBM SPSS Statistics. 5th edn. London: Sage.

Howitt, D. and Cramer, D. (2020) Introduction to Statistics in Psychology. 7th edn. Harlow: Pearson.

Pallant, J. (2020) SPSS Survival Manual. 7th edn. Maidenhead: Open University Press.

Paulhus, D.L. (1991) ‘Measurement and control of response bias’, in Robinson, J.P., Shaver, P.R. and Wrightsman, L.S. (eds) Measures of Personality and Social Psychological Attitudes. San Diego: Academic Press, pp. 17–59.