A paper concludes that “using social media for more than three hours a day increases the risk of depression in students”. Table 3 shows three models. In Model 1 the odds ratio is 1.9. In Model 3, after adjusting for sleep, physical activity and academic stress, it is 1.15, with a 95% confidence interval of 0.92 to 1.44, and the sample has shrunk from 2,140 to 1,610. The abstract mentions only 1.9.
The abstract tells you what the authors want you to think. The results table tells you what the data actually say. This skill is useful when writing a literature review, when reviewing for a journal and when checking your own tables before submission.
Step 1: read the title and footnotes first
The table title and footnotes tell you the outcome, the model type, what the numbers in each cell are (coefficients, odds ratios, means), what the asterisks mean and which variables were adjusted for. A surprising number of misreadings come from interpreting a number without knowing whether it is a log-odds coefficient or an odds ratio.
Step 2: identify the estimate type and its null value
| Estimate | “No association” value | Interval indicates significance when |
|---|---|---|
| Linear regression coefficient, mean difference | 0 | It excludes 0 |
| Logistic coefficient on the log-odds scale | 0 | It excludes 0 |
| Odds ratio, risk ratio, hazard ratio | 1 | It excludes 1 |
| Correlation coefficient | 0 | It excludes 0 |
With ratios, remember the asymmetry: an OR of 0.5 and an OR of 2.0 represent associations of equal strength in opposite directions. Confidence intervals for ratios are usually lopsided, for example 1.2 to 3.1 around an estimate of 1.9, and that is normal.
Step 3: compare crude and adjusted estimates
Many tables show “crude” (unadjusted) and “adjusted” columns, or Models 1, 2 and 3 adding variables in stages. Watch how the estimate moves:
- It drops sharply as variables are added: part of the original association is explained by them, as in the opening example.
- It barely changes: the association is robust to the variables adjusted for.
- It increases: there may be a suppressor variable, and the discussion deserves a close read.
Always ask which variables were adjusted for and whether any lie on the causal pathway. Adjusting for a mediator, such as sleep when sleep may be one route by which social media affects mood, can hide the very association under study. That is a design debate rather than a calculation error, but readers need to see it.
Step 4: check the sample size in each model
The N at the bottom of each column is easily overlooked. If N falls across models, the usual reason is missing data in newly added variables: software silently drops anyone missing any variable. The models are then fitted to different groups of people, and changes in the coefficient may reflect a change in sample rather than adjustment. Careful authors fit every model to the same sample or handle missing data with an appropriate method.
Step 5: look at interval width, not just asterisks
Two estimates with the same asterisk can differ greatly in precision: OR 2.1 (1.9 to 2.3) versus OR 2.1 (1.02 to 4.3). The second is compatible with anything from a negligible association to a very strong one. If a table shows only asterisks, with no confidence intervals or standard errors, that is a weakness worth noting in a review.
Step 6: read the ANOVA line
A typical ANOVA result is reported as F(2, 117) = 5.84, p = 0.004, η² = 0.09. How to read it:
- F: the ratio of between-group to within-group variance.
- Degrees of freedom (2, 117): the first is the number of groups minus one, so three groups; the second is total observations minus the number of groups, so 120 people. A quick way to check the sample matches the methods section.
- η² (eta squared): the factor explains about 9% of the variance. In multi-factor ANOVA, software usually reports partial η², which cannot be compared directly across different designs.
A significant F only tells you that at least one group differs from the others. To know which, look at the post hoc comparisons and the adjustment method used.
Step 7: check the table against the text and abstract
- Does the figure in the abstract come from the main model, or from the more impressive crude model?
- Does the discussion use causal language when the table reports cross-sectional data?
- Have non-significant variables quietly disappeared from the table? A table containing nothing but asterisks is a warning sign.
- Do totals and Ns agree across tables?
In practice: reading a table in five minutes
When you meet a results table, work through these steps and jot one line for each:
- Outcome and model type, from the title and footnotes.
- Estimate type and null value.
- Main estimate: crude value, adjusted value, and what it was adjusted for.
- Whether N is the same across models.
- How wide the confidence interval around the main estimate is.
- For ANOVA: do the degrees of freedom match the sample, is there an effect size, are there post hoc tests?
- Whether the abstract’s conclusion matches the main model.
After a few dozen tables the routine becomes automatic. Applied to your own tables before submission, it catches exactly the problems reviewers would otherwise find.
Next step: pick the most important paper in your literature review, run the seven steps on its main results table, and check whether the claim you cite from it actually matches the authors’ main model.
Câu hỏi thường gặp
How do I know if an odds ratio confidence interval is significant?
For odds ratios, risk ratios and hazard ratios, the no-association value is 1. If the 95% confidence interval excludes 1, the result is significant at the 5% level.
What is the difference between crude and adjusted estimates?
A crude estimate includes only the exposure of interest; an adjusted estimate adds potential confounders. Comparing them shows how much of the original association those variables explain.
Why does the sample size change between regression models?
Usually because of missing data in newly added variables, since software drops any observation missing a variable. The models are then fitted to different groups of people.
What does F(2, 117) mean in ANOVA?
The two numbers are degrees of freedom: the first is the number of groups minus one, the second is total observations minus the number of groups. This example implies three groups and 120 people.
What is the difference between eta squared and partial eta squared?
Eta squared uses total variance, while partial eta squared removes variance due to other factors. Partial eta squared is usually larger and cannot be compared directly across designs.
