MKF2121 Chap.4 Data Preparation and Tests of Differences
Data Preparation and Tests of Differences
Difference testing begins with auditable preparation. This chapter preserves missing states, coding direction, case rules and derived variables before selecting one-sample, independent, paired or multi-group comparisons. Every result is interpreted through the hypothesis decision, observed direction, magnitude, uncertainty and marketing consequence rather than through a p-value alone.
What this chapter covers
- 01
Codebooks, missing states and preparation logs
- 02
Hypotheses, thresholds and p-value meaning
- 03
Independent-samples t tests and variance rows
- 04
Paired-samples t tests and difference direction
- 05
One-sample comparisons with benchmarks
- 06
One-way ANOVA and the omnibus alternative
- 07
Eta-squared and planned comparisons
- 08
Assumptions, unusual values and robust choices
- 09
Practical importance and uncertainty
- 10
Marketing-language result paragraphs
Interpret a paired concept comparison
- 2Name the paired observation structure and subtraction order.
- 2State the null decision, direction and mean difference without treating p as magnitude.
- 2Add uncertainty, order effects, population boundary and practical consequence.
Key terms
- Null hypothesis
- The population statement of no specified difference or association evaluated by a statistical test.
- P-value
- A measure of result compatibility with the null model under its assumptions.
- Independent t test
- A mean comparison between two groups whose observations are independent.
- Paired t test
- A mean comparison performed on linked within-pair differences.
- One-way ANOVA
- An omnibus comparison of three or more independent population means.
- Eta-squared
- The proportion of observed variation allocated to group differences in an ANOVA decomposition.
Data Preparation and Tests of Differences FAQ
What does a displayed p-value of .000 mean?
It is rounded output rather than a probability literally equal to zero. Report it as p below .001 and keep the result tied to the test assumptions, estimate and research design.
What does a significant one-way ANOVA establish?
It rejects the joint null that all population means are equal, showing that at least one differs. It does not establish that every pair differs, so inspect planned contrasts or adjusted post-hoc comparisons with group estimates.
How is Levene's test used in an independent t test?
It informs the variance-assumption row used for the mean comparison. Its p-value is not the substantive test of group means; the analyst selects the appropriate row and then reads that row's t-test evidence.
Assessment move
Build a test-selection map from observation structure: one sample against a justified benchmark, two independent groups, linked pairs, or several independent groups. For every output, identify the correct row and write a three-layer interpretation covering the null decision, observed direction and magnitude, and marketing meaning with its design boundary.
Recompute subtraction signs and eta-squared, report software .000 as p below .001, and never write that all means differ from an omnibus result alone. Start every practice set with a miniature codebook. Define allowed values, missing states, scale direction and any derived score. Write exclusion rules before looking at group outcomes and preserve a case-flow count.
This makes statistical interpretation traceable to preparation rather than treating the software file as self-explanatory. Next classify the observation structure without naming a test: one sample against a benchmark, two independent groups, linked scores or several independent groups. Only then choose the procedure and state its null in words.
For independent tests, read Levene's result solely to select the variance row, then locate the mean-test p-value. For paired tests, calculate the difference column in the stated order and explain the sign. For ANOVA, state that the alternative is not all population means are equal, calculate eta-squared from between-group over total variation and reserve pair claims for planned or adjusted comparisons.
Write every result twice: first as a statistical decision with means, difference, interval or effect size; second as a marketing interpretation with population, period, design boundary and practical consequence. Compare the versions to ensure that causality, equality or importance was not added during translation.
Treat displayed .000 as a rounded value and report p below .001. Finish by recomputing all anchors, checking consistent rounding and locating every place the number appears in the worked answer, caption, summary and recommendation. Any disagreement sends you back to the analysis rather than to a verbal compromise. Use a final output-to-prose check.
Point from every sentence to the exact mean, difference, interval, p-value or effect size that supports it, and from that statistic back to the prepared cases. Confirm group order, units and eligible denominator. If the interpretation cannot be traced in both directions, reopen the analysis. This catches confident wording built from the wrong row or sign.
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