WORK6010 Chap.3 Hypotheses, Descriptives and t-Tests
Hypotheses, Descriptives and t-Tests
Hypothesis testing formalises a comparison, but it does not replace descriptive understanding or practical judgment. This chapter moves from variable type and design to summaries, null and research hypotheses, independent and paired t tests, test statistics and cautious conclusions.
The central discipline is to state exactly what was compared and avoid turning a probability statement into proof of a mechanism or business value.
What this chapter covers
- 01
Write compatible null and research hypotheses for a mean comparison
- 02
Use means, standard deviations and distributions before inferential testing
- 03
Choose an independent or paired t test from the sampling design
- 04
Interpret a p value as evidence under a stated null model
- 05
Report effect magnitude and uncertainty alongside statistical significance
- 06
Translate a result into an HR decision without claiming causation automatically
Worked example · free
Compute and interpret a paired change
- +1The marks used in this calculation are not an official assessment scheme. After-minus-before differences are 2, 1, 1 and 2.
- +1Mean difference = 6 divided by 4 = 1.5 confidence points.
- +1Deviations from 1.5 are 0.5, negative 0.5, negative 0.5 and 0.5.
- +1Squared deviations sum to 1.00, so sample variance = 1.00 divided by 3 = 0.333.
- +1Sample standard deviation = square root of 0.333 = 0.577, approximately 0.58 points. Pairing is required because the same employees were measured twice.
Key terms
- Null hypothesis
- The reference claim evaluated by a statistical test, often no population mean difference.
- Research hypothesis
- The expected pattern or difference that motivates the analysis.
- Paired t-test
- A mean comparison based on differences from linked observations such as repeated measures on the same people.
- Independent t-test
- A mean comparison between separate groups when the observations are appropriately independent.
- Practical significance
- The decision relevance or substantive size of a result rather than its statistical detectability alone.
Hypotheses, Descriptives and t-Tests FAQ
How do I choose between paired and independent t tests?
Follow the design. Use paired reasoning when each value in one condition has a meaningful partner, such as the same employee before and after training or matched cases. Use independent reasoning for separate groups. The variable names do not decide the test; the relationship among observations does.
Does a small p value prove the research hypothesis?
No. It indicates that the observed result would be unusual under the specified null model, subject to assumptions. It does not prove a mechanism, remove bias or show business importance. Report the comparison, magnitude, uncertainty, design and plausible alternatives before recommending action.
Why report descriptive statistics first?
Means and standard deviations reveal scale and spread, while distributions can expose outliers, skew or coding errors. A test result without descriptive context hides what changed. Descriptives also help verify that the planned method matches the data and let a reader judge practical importance.
What belongs in a complete t-test conclusion?
Name the groups or paired occasions, direction and magnitude of the observed difference, statistical evidence and uncertainty, then identify the design limitation. Avoid saying the test proves importance or causation. Translate the result back into the original workforce scale so a reader can judge whether the difference could support action.
Exam move
Make a decision tree with two questions: is the outcome numeric, and are observations linked or separate? Practise writing hypotheses before calculating. For each fresh dataset, show the mean and standard deviation, sketch the direction of the comparison, and create a paired difference column when relevant. After reading a p value, force yourself to add two independent sentences: one on magnitude and one on design limitations.
In timed practice, label every statistic with its group or time point and use the phrase 'the observed data support' instead of 'prove'. This keeps the conclusion aligned with the actual evidence. Create small datasets by hand and calculate the paired differences before using any output. Change one after score, then explain how the mean difference and spread respond.
Contrast that exercise with two independent groups so the source of each observation remains obvious. Write the null and research hypotheses in words and symbols, but return to workforce units in the conclusion. Review outliers by asking whether they are errors, genuine cases or evidence that the average masks distinct experiences.
Finally, draft three versions of the same result: statistically detectable but trivial, practically large but uncertain, and both meaningful and precise. This stops significance from becoming a universal decision rule.
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