Effect size is a number that tells you how large a difference or relationship actually is, separate from whether it is statistically significant. Where a p-value only says whether an effect is likely to be real, effect size says how much it matters in practical terms. In your dissertation it is the figure that turns a bare test result into a claim the reader can judge.
Why significance alone is not enough for your thesis
A result can be statistically significant and still be trivially small, because significance depends heavily on sample size. With a few thousand participants almost any difference will cross the threshold, even one too tiny to care about. That is exactly why examiners look for an effect size alongside every test: it answers the question the p-value cannot, namely how big the effect is. If you have only read how to read a p-value, you have done half the job; the effect size is the other half of a defensible result. The effect size calculator works out Cohen's d, eta-squared, and the odds and risk ratios from your own figures.
The common effect size families you will report
Different designs call for different metrics. For a difference between two group means you usually report Cohen's d, which expresses the gap in standard deviation units. For a relationship between two continuous variables you report Pearson's r, the correlation coefficient. For an analysis of variance you report eta squared or partial eta squared, the share of variance explained. For a regression you lean on R squared, and for a contingency table you use Cramer's V or an odds ratio. Each one travels with its own conventional benchmarks for small, medium, and large.
Cohen's d, eta squared, and other effect size measures
It helps to group the measures by what they answer. The standardised mean difference family, led by Cohen's d and the bias-corrected Hedges' g, expresses a gap between two means in standard deviation units, so a d of 0.6 means the groups sit 0.6 standard deviations apart. The variance-explained family, including eta squared (η²), partial eta squared, and R squared, reports the proportion of variation in the outcome that your factor or model accounts for. The correlation family, Pearson's r and Cramer's V, scales effects between 0 and 1.
Choosing within these families is mostly driven by your design. A t-test or one-way ANOVA pairs naturally with d or η², a correlation with r, and a contingency table with Cramer's V or an odds ratio. You can produce each of these from your own summary figures with the Cohen's d and eta squared calculator, which keeps the metric consistent with the test you actually ran.
Interpreting small, medium, and large effects
Benchmarks make a raw number meaningful, but they are guides rather than verdicts. For Cohen's d, 0.2 is conventionally small, 0.5 is medium, and 0.8 or above is large. For Pearson's r the rough cut points are 0.1, 0.3, and 0.5, while for eta squared they fall near 0.01, 0.06, and 0.14. The sign of d or r tells you direction, not strength, so a d of -0.7 is a large effect in the negative direction.
Read these labels against what is normal in your field rather than treating them as fixed law. In an area where most published effects are small, a "medium" result may be genuinely important, and in a tightly controlled experiment a large effect might be unremarkable. This is also why an effect size should travel with a confidence interval for the effect: a wide interval can stretch a single point estimate across two benchmark categories, warning you not to over-claim the label.
Reporting effect size in APA style
APA expects the effect size in the same sentence as the test statistic and the exact p-value, written with the correct symbol and, where conventional, a confidence interval. Italicise the symbols, so d, r, and R² are all italic, and drop the leading zero from values that cannot exceed one, for example r = .42 rather than 0.42, while Cohen's d does keep its leading zero because it can exceed one. A clean line reads like t(48) = 2.71, p = .009, d = 0.78.
Place the figure where the reader meets the result, not in a distant footnote, and state in words what the value means for your research question. The full set of spacing, italics, and decimal conventions lives in the APA format for reporting results, and you can have the line assembled for you with the APA results formatter.
Notice in the layout above that the effect size is the final term in the line, not an afterthought. It belongs in the same sentence as the test statistic and the exact p-value, which is why a clean write-up reports all three together. The benchmarks you attach matter too: a Cohen's d near 0.2 is small, around 0.5 is medium, and 0.8 or higher is large, though your field may set its own expectations.
How effect size connects to power and precision
Effect size is not only a reporting figure; it drives your study before you collect a single data point. The smaller the effect you expect, the larger the sample you need to detect it, which is the heart of statistical power. Plan around an effect that is realistic for your area, not an optimistic one, or your study risks being underpowered. After the fact, every effect size carries uncertainty, which you express with a confidence interval around the estimate. A wide interval signals that your sample was too small to pin the effect down, even if the point estimate looks large.
Reporting effect size in your results chapter
Report the effect size for every inferential test, give its confidence interval where the convention allows, and interpret it in plain language rather than leaving the reader to look up the benchmark. State the metric by name, the value, and what it means for your research question. Follow the guidance on presenting statistics in APA format so the value, its sign, and the absence of a leading zero are all correct. Done well, the effect size is the sentence your supervisor remembers, because it is the one that says how much your finding actually matters.