WORK6010 Chap.4 ANOVA, Regression and Results
ANOVA, Regression and Results
ANOVA and regression answer different versions of the question 'what varies with the outcome?' This chapter selects a method from the outcome, predictors, design and research purpose. It explains the omnibus logic of ANOVA, the conditional interpretation of regression coefficients and the difference between model fit and causal validity.
Reporting ends with an audience-ready result, not a software table copied without interpretation.
What this chapter covers
- 01
Use ANOVA for mean comparisons across defined groups or conditions
- 02
Interpret an omnibus result before examining planned or post hoc contrasts
- 03
Use regression to estimate outcome relationships with several predictors
- 04
Read coefficients conditionally while holding other included predictors constant
- 05
Separate model fit, predictive performance, statistical uncertainty and causal claims
- 06
Report magnitude, reference categories, limitations and the decision implication
Worked example · free
Read a multiple regression coefficient
- +1This mark allocation is not an official University marking scheme. Training contribution = 3.2 times 4 = 12.8 performance points.
- +1Tenure contribution = 0.8 times 5 = 4.0 performance points.
- +1Predicted performance = 52 + 12.8 + 4.0 = 68.8.
- +1The training coefficient means one additional training hour is associated with 3.2 higher predicted points when included tenure is held constant.
- +1Training participation may reflect motivation, manager support or role, so an observational coefficient does not establish the effect of assigning training.
Key terms
- Omnibus test
- A test of whether a set of group means shows evidence of at least one difference without identifying every differing pair.
- Post hoc contrast
- A follow-up comparison used after an omnibus result, with attention to multiple testing.
- Regression coefficient
- A conditional estimate linking a predictor change to an outcome change within the specified model.
- Reference category
- The comparison category against which categorical predictor coefficients are interpreted.
- Model fit
- A description of how well a model represents observed outcomes, distinct from causal validity or future performance.
ANOVA, Regression and Results FAQ
When is ANOVA preferable to several t tests?
When the research question compares means across several groups or conditions, ANOVA supplies a single omnibus test and a coherent variance framework. Repeated pairwise tests inflate the opportunity for false positives. Planned or adjusted follow-up comparisons can then answer the specific substantive questions.
What does holding other predictors constant mean?
It means the coefficient compares cases that have the same values on the other predictors included in the model. This is a mathematical conditional comparison, not proof that all relevant differences were controlled. Omitted variables, measurement error and selection can still distort interpretation.
Should I report only statistically significant predictors?
No. Report the model purpose, sample, outcome scale, key estimates, uncertainty and limitations. Selective reporting hides the analysis context and can exaggerate certainty. A predictor can be statistically detectable but too small, unstable or unfair for the intended HR decision.
How should an interaction be reported?
Show the relevant group means or predicted values and explain how the pattern changes across the second factor. Do not interpret an averaged main effect as universal when simple patterns differ. Report uncertainty and connect the interaction to a defined decision, while keeping observational design limits separate from the model calculation.
Exam move
Build a method table organised by question rather than software menu. Use rows for comparing means, estimating associations, predicting new cases and evaluating change. For every ANOVA scenario, write the factors, outcome and exact contrast that matters before discussing significance. For every regression scenario, calculate one prediction and interpret one coefficient with its units and reference conditions.
Practise translating a model output into three reader levels: a technical sentence, a manager sentence and a caution sentence. This develops the communication skill assessed by WORK6010 and prevents results sections from becoming lists of numbers without a decision. Draw group means before reading an ANOVA table and sketch two possible interactions with the same average main effect.
For regression, annotate the intercept, coefficient units, reference category and observed predictor range. Recalculate a prediction after changing only one input so conditional interpretation becomes automatic. Compare a high in-sample fit with weak later-cohort performance to reinforce that explanation and prediction are separate claims.
When reviewing a result, circle the specific estimate that answers the business question and cross out every statistic that does not change the recommendation. End with a limitation linked to design or measurement and a concrete validation step rather than the vague phrase 'more research is needed'.
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