FOOD9102 Chap.7 Analysing Hedonic Data with t-Tests and ANOVA
Analysing Hedonic Data with t-Tests and ANOVA
Hedonic data are numbers, so products are compared through their mean scores and spread. This chapter shows how to set up a t-test for two samples, how the wording of the research question decides between one and two tails, and why ANOVA with multiple comparisons replaces a string of t-tests when there are three or more samples.
It works a two-tailed t-test on two muesli bars and drills the reading of t-test and ANOVA outputs, always ending with a conclusion about the products.
The workshop’s apple and orange juice questions follow the same arc as this chapter: decide the test, decide the tails, compute the means and errors, find the p-value, plot the result and conclude.
Practising that arc is the best preparation for the hedonic laboratory report.
What this chapter covers
- 01
Comparing two means with their error
- 02
One-tailed and two-tailed tests from the research question
- 03
Running a t-test in Excel or an online calculator
- 04
ANOVA for three or more samples
- 05
Reading overall and pairwise p-values
- 06
Plotting means with standard deviation error bars
Worked example · free
Lower-fat crisps: one tail or two?
- 1The question predicts a direction, liked less, so a one-tailed test is appropriate.
- 1One-tailed p = 0.03 < 0.05: the lower-fat crisp is liked significantly less than the original.
- 1A two-tailed test would give about double, p = 0.06, which would not be significant; the tails must be fixed before the data are seen.
Key terms
- t-test
- A t-test compares the means of two samples, taking their spread into account, and returns a p-value.
- One-tailed test
- A one-tailed test checks for a difference in one stated direction only.
- Two-tailed test
- A two-tailed test checks for a difference in either direction when none is predicted.
- Analysis of variance
- Analysis of variance, or ANOVA, compares the means of three or more samples in one test.
- Multiple comparisons
- Multiple comparisons are the pairwise tests that follow an ANOVA to show which samples differ.
- Unpaired t-test
- An unpaired t-test compares the means of two independent sets of scores, as in the lecture's worked output.
Analysing Hedonic Data with t-Tests and ANOVA FAQ
Why not just run t-tests between every pair of samples?
With three samples you would need three t-tests, and the number grows quickly as products are added. ANOVA compares the variance among all the means at once, then its multiple comparisons show which pairs differ, which the lecture presents as the faster route.
What if the overall ANOVA is not significant but one pair looks different?
Report that there is no significant difference among the samples. The overall test comes first; searching the pairwise comparisons for a significant result after a non-significant overall test overstates the evidence.
How should I present hedonic results in a report?
Report each mean with its standard deviation, plot them as bars with error bars, state the test and its p-value, and finish with a sentence about which product was liked more, or that liking did not differ. The graph and the statistic should tell the same story.
Do I need to calculate a t statistic by hand?
No. The workshop uses the T.TEST function in Excel or an online t-test calculator. What you must supply is the right choice of test and tails, the correct data, and a conclusion; the output then gives you the p-value to compare with alpha.
Assessment move
Work the workshop problems again with your own invented numbers, using both Excel and an online calculator so you can check one against the other. Before each calculation, write down the tails and why. Practise writing three-sentence conclusions for ANOVA outputs, overall result first and pairs second. Check every conclusion against its graph before you submit.
For the report, include the calculator or spreadsheet output in an appendix so the marker can see exactly which test you ran.
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