In short
A hierarchical regression is reported block by block, and what justifies it is not the coefficients but the increment: for each step you give the change in explained variance and its change test, ΔR² = .09, ΔF(1, 196) = 23.44, p < .001. The final model is summarized with its total R² and F, and coefficients go in a table with one column per step. Without the ΔR² values you have run a multiple regression with decorative steps.
Hierarchical regression is the analysis most often misreported in psychology: it is built in blocks and then written up as an ordinary multiple regression, so the reader cannot tell what each step adds. Here is which numbers APA 7 requires, how to build the step table, and what makes a reviewer stop. The general guide is in how to report results in APA 7, and single-block regression in how to report a regression.
What makes it hierarchical rather than multiple
In a multiple regression you enter every predictor at once and ask which one weighs most. In a hierarchical regression you enter them in an order you decide a priori, for a theoretical reason, and the question is different: does the new block explain variance over and above what the previous block already explained?
That question is answered by a number multiple regression does not have: the change in R². This is why the write-up revolves around ΔR² and its F change test, not around the betas. If no ΔR² appears anywhere in your manuscript, the reviewer will conclude — correctly — that the steps are decorative and an ordinary regression would have done.
Watch one common confusion: hierarchical is not stepwise. In hierarchical regression theory decides the order; in stepwise an algorithm decides it from significance values. Stepwise is poorly regarded in psychology because it capitalizes on sample noise, and if you use it you will be asked to justify or replace it.
What to report for each step
For each block: the cumulative R² up to that point, the change ΔR², the F change test with both degrees of freedom, and its p value. The degrees of freedom for the F change are the number of predictors entering at that step and the residual degrees of freedom of that step’s model.
For the final model: total R², adjusted R² and the overall F with its degrees of freedom. And for each predictor in the final model: the unstandardised coefficient B, its standard error, the standardized β, t, p and — increasingly expected — the 95 % confidence interval for B.
One detail authors always forget: state which predictors enter at each step and why in that order. Without that sentence the hierarchy has no ground to stand on. The usual pattern is covariates or control variables first (age, sex, baseline severity) and the variables of interest afterwards.
Example in the text
"A two-step hierarchical regression was estimated. Age and sex were entered as covariates in Step 1 and explained 6 % of the variance in well-being, R² = .06, F(2, 197) = 6.29, p = .002. Self-esteem was added in Step 2 and significantly increased the explained variance, ΔR² = .09, ΔF(1, 196) = 23.44, p < .001. The final model explained 15 % of the variance, R² = .15, adjusted R² = .14, F(3, 196) = 11.53, p < .001. Self-esteem was the only significant predictor in the final model, B = 0.38, SE = 0.08, β = .32, t(196) = 4.84, p < .001, 95 % CI [0.22, 0.54]."
Note the formatting: R, F, B, SE, t and p in italics; the Greek β upright; and the leading zero only on statistics that can exceed 1 (B = 0.38 keeps it, R² = .15 and β = .32 do not).
If what you are looking at is the block of tables SPSS produces — Model Summary, ANOVA, Coefficients — and you cannot see where each figure comes from, paste the output into the interpreter and it breaks it down in exactly this format.
The step-by-step table
A hierarchical table has one column per step, with predictors as rows. Each column holds that model’s coefficients (usually B with its SE, or β), and the foot of each column repeats R², ΔR² and ΔF. That way the table reads left to right, showing how each coefficient shifts as the next block enters — usually the interesting part.
APA formatting: horizontal rules at the top, under the headings and at the foot; no vertical rules; significance asterisks explained in the note. If you would rather have it built for you, the APA 7 regression table generator produces it ready to paste.
One recommendation that saves arguments with reviewers: show the coefficients for every step, not just the last one. A predictor losing significance when the next block enters is information, not a problem to hide.
What reviewers flag
Not reporting the ΔR² values. This is the number one error and it leaves the design unjustified: no increment, no hierarchy.
Giving ΔF without its degrees of freedom. Nothing can be recomputed without them, and automated checkers look for exactly this.
Justifying the order after the fact. If the order was decided after looking at the results, that is HARKing and it shows. Order is argued from theory, not from p values.
Too many blocks with a small sample. Every step consumes degrees of freedom and multiplies comparisons. With N = 80 and four blocks, the final model means very little.
Ignoring multicollinearity. Blocks are usually correlated with each other; report VIF values in the text or in a note.
Frequently asked questions
What exactly is ΔR² and why is it required?
It is the additional variance a block explains over and above everything the previous blocks already explained. It is the only number that justifies entering predictors in steps: without it the hierarchy adds nothing to an ordinary multiple regression and the reader cannot evaluate your hypothesis.
How do I report the F change and which degrees of freedom does it take?
Report it as ΔF(df1, df2) = value, p. The first degree of freedom is the number of predictors entering at that step; the second is the residual degrees of freedom of that step’s model. For example, if one predictor enters at Step 2 in a sample of 200 with three predictors in total: ΔF(1, 196) = 23.44, p < .001.
Is hierarchical regression the same as stepwise?
No, and confusing them is a problem. In hierarchical regression you decide the entry order yourself, for theoretical reasons, before looking at the data. In stepwise an algorithm decides it from each predictor’s significance. Stepwise is poorly regarded in psychology because it capitalizes on sample noise and its results rarely replicate.
Do I report coefficients for every step or only the final model?
For every step, in a table with one column per step. A predictor losing significance when the next block enters is often the interesting finding, and hiding it by showing only the final model is what makes a reviewer ask for your data.
How many participants does a hierarchical regression need?
It depends on the effect size you expect and the total number of predictors, not on the number of blocks. A common rule of thumb is 10 to 15 cases per predictor, but the correct approach is an a priori power analysis for the R² increment you want to be able to detect, not for the overall model.
Do assumptions need reporting in a hierarchical regression?
Yes, and two sentences are enough: linearity, independence of residuals, homoscedasticity and normality of residuals, plus what you did if one failed. Add VIF values, because blocks in a hierarchical model are usually correlated: above 10 there is a clear problem and many authors already worry from 5.
Your ΔR² values are there, but does the order hold up?
The order of the blocks is the first thing a reviewer argues with, and it cannot be fixed in the response letter: it is fixed before you submit.
Run it through the paper reviewer →With the ΔR² values, the ΔF and its degrees of freedom, and the step table, your hierarchical regression is reported the way APA 7 asks. If the model gets complicated — cross-block interactions, nested data, mediation — we can work through it in my statistical consulting.