FOOD9102 Chap.3 Statistics for Sensory Data: p-Values, Alpha and Error
Statistics for Sensory Data: p-Values, Alpha and Error
Every sensory claim in this course ends in a statistical judgement. This chapter revisits the Week 1 workshop toolkit: statistics as evidence rather than proof, the normal distribution and its tails, the p-value as the probability of a result at least this extreme by chance, the alpha level of 0.05, and standard deviation as the measure of error that decides whether two means really differ.
A worked example takes eight panellists’ scores for two yoghurts from raw numbers to a reported verdict.
Nothing here requires heavy calculation: the course leaves the arithmetic to calculators and spreadsheets. What it does require is that you can explain what each number means and use it to reach a sentence about the products.
What this chapter covers
- 01
Statistics as evidence that a result is not luck
- 02
Why forced-choice tests need a guessing baseline
- 03
The normal distribution and its tails
- 04
The p-value, alpha and statistical significance
- 05
Standard deviation, error bars and reporting mean plus or minus SD
- 06
How error decides whether a difference is significant
Worked example · free
Report and interpret two crispbread liking scores
- 1Means: 69/10 = 6.9 for crispbread 604 and 58/10 = 5.8 for crispbread 291.
- 1Standard deviations: 0.74 and 0.63, so report 6.9 ± 0.7 and 5.8 ± 0.6.
- 1Compare: p = 0.0021 is below 0.05, so the difference is statistically significant.
- 1Conclude: panellists liked crispbread 604 more than crispbread 291.
Key terms
- Null hypothesis
- The null hypothesis is the starting assumption that the samples do not differ, which the p-value tests.
- Statistical significance
- Statistical significance is the outcome when the p-value falls below the chosen alpha level.
- Standard deviation
- Standard deviation is the usual measure of error in sensory science, describing how widely scores scatter around their mean.
- Normal distribution
- The normal distribution is the bell-shaped curve against which the probability of an outcome is judged.
- Error bars
- Error bars are the lines on a graph that show the standard deviation around each mean.
- Sample mean
- The sample mean is the average score of a panel for one product, reported together with its standard deviation.
Statistics for Sensory Data: p-Values, Alpha and Error FAQ
What does p < 0.05 actually mean?
It means that a result at least this extreme would occur less than 5% of the time if chance alone were at work. That is strong enough evidence, by the usual convention for sensory data, to call the difference real. It is evidence rather than proof, and the conclusion should say what it means for the samples.
Why does the spread of the scores matter if the means are different?
Because a gap between two means can come from natural variation between panellists. If scores are widely spread, the two distributions overlap and the gap is more plausibly chance; if they are tightly packed, the same gap is much more convincing. The error therefore drives the p-value.
Should I report the exact p-value or just p < 0.05?
The workshop accepts either: report p < 0.05 for a significant result or p > 0.05 for a non-significant one, or give the exact value. The exact value carries more information, because a lower p-value means you can be more confident that the difference is real.
Is a smaller p-value always better?
A smaller p-value means stronger evidence that a difference is real, because the result would be less likely under chance alone. Whether that is good news depends on the objective: a company hoping a reformulation goes unnoticed wants no significant difference, so a very small p-value is a warning rather than a success.
Assessment move
Make a one-page sheet with the five definitions from the workshop, the decision rule and a sketch of two overlapping distributions. Then compute mean and standard deviation by hand for a small data set once, so you know what a calculator is doing, and practise writing the four-part conclusion until it is automatic. Finally, keep a habit of rounding consistently, usually one decimal place for means and SD on a 9-point scale.
If you are rusty on statistics, the recommended text explains the tests used in the course well, even though it assumes a high level of prior knowledge.
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