Reporting Quantitative Results in Chapter 4 of Your Thesis or Dissertation

A quantitative results chapter succeeds when a reader can check every claim against a number, and every number against a table. Your committee includes at least one member who will do exactly that. The chapter is not the place to show how much analysis you ran. It is the place to answer each research question or hypothesis with the evidence that bears on it.

This article assumes you have already chosen your tests in Chapter 3. For the general shape of the chapter, see Chapter 4: what to include. What follows concerns the statistics themselves.

The order of the chapter

Most quantitative chapters run in this sequence:

1. Data preparation and screening. Report how many cases you collected, how many you removed and why, how you treated missing data, and what you did about outliers. A reader cannot trust your results without knowing which cases they rest on.
2. Sample description. Give the final sample size and the characteristics that matter to the study, usually in a table.
3. Descriptive statistics. Means, standard deviations, ranges, and frequencies for the main variables.
4. Reliability of the instruments. For multi-item scales, report an internal consistency estimate such as Cronbach's alpha from your own data, even when the original authors reported one.
5. Assumption checks. State which assumptions each test requires, how you checked them, and what you found. Say what you did when an assumption failed, for example using a nonparametric test or a method built for that violation.
6. Results for each research question or hypothesis. One heading per question, in the order they were introduced.
7. A short summary that gathers the findings and leads into Chapter 5.

Reporting each test

For every test, give four things: the test, the statistic with its degrees of freedom, the exact probability value, and an effect size. Then say what the result means in plain words.

Sample wording shows the pattern. The numbers below are illustrative, so use your own output.

• A comparison of two groups: "Participants who received mentoring (M = 4.12, SD = 0.61) reported higher commitment than those who did not (M = 3.71, SD = 0.68), t(58) = 2.31, p = .024, d = 0.60."
• A comparison of three groups: "Commitment differed across the three school types, F(2, 117) = 4.52, p = .013, η² = .07."
• A correlation: "Workload was positively related to intention to leave, r(98) = .34, p < .001."

In each sentence the reader learns the direction of the result, the size of the difference or relationship, and whether it passed the threshold you set in Chapter 3. Say which threshold you used, usually .05, and keep to it.

Effect sizes and significance

A significant result tells the reader that an effect is unlikely to be zero in the population. It does not tell them how large the effect is. With a large sample, a trivial difference can reach significance. With a small one, a difference that matters can miss it. So report an effect size beside each test and interpret it.

Cohen's widely cited benchmarks treat a d of 0.2 as small, 0.5 as medium, and 0.8 as large. For correlations the corresponding values are .1, .3, and .5. For eta squared they are .01, .06, and .14. These are conventions and not laws, so interpret an effect in the light of your field and your outcome. Add confidence intervals where your program asks for them.

For a non-significant result, state it as it is. "The difference was not statistically significant" is accurate. "There was no difference" is not, because a non-significant test cannot show that an effect is absent. If your sample is small, say that power was limited and keep the interpretation for Chapter 5.

APA 7 formatting for statistics

If your program uses APA 7, these conventions apply:

• Italicize statistical symbols: M, SD, t, F, p, r, N, n, and d. Greek letters such as η² are not italicized.
• Report exact p values to two or three decimals. Use p < .001 for smaller values, and never write p = .000.
• Omit the leading zero for values that cannot exceed 1, such as p and r (p = .024, r = .34). Keep it for values that can, such as d and t (d = 0.60).
• Put degrees of freedom in parentheses after the symbol, as in t(58).
• Write out numbers below ten in text, except for statistics and measurements.

Avoid "highly significant," "marginally significant," and "proves." The first two have no standing in the framework you set in Chapter 3, and the last overstates what any single study can show.

Tables and figures

Put the full detail in tables and state the main point in the text. Number each table, give it a short descriptive title, and refer to it by number in the sentence that introduces the finding. In APA 7 the table number appears above the table in bold, with the title below it in italic title case, and notes go below the table. Do not repeat every number from a table in the paragraph above it.

Before submitting, check three things. Every number in the text matches the table it comes from. Degrees of freedom agree with the sample sizes you reported. And the tests you describe in Chapter 4 are the ones you described in Chapter 3. A mismatch of this kind is one of the quickest ways to lose an examiner's confidence.

Keeping interpretation for Chapter 5

Chapter 4 reports what the numbers show. Why they came out that way, how they compare with earlier studies, and what they mean for practice belong in Chapter 5, unless your program combines the two. For the matching guidance on qualitative work, see our article on presenting themes clearly.

If you want an outside check on whether your tests suit your questions and your results are reported consistently, our research design and methodology review examines the design and analysis plan, and a chapter review examines the written chapter. The findings stay yours.