BPS3082 Chap.1 Statistical Decisions for Experimental Data
Statistical Decisions for Experimental Data
This chapter turns experimental design into a defensible analysis. It separates independent units from technical repeats, distinguishes SD from SEM, checks normality and equal-variance assumptions, and uses pairing and group count to choose a t-test or ANOVA. The central skill is conclusion control: a global ANOVA can show that not all means are equal but cannot identify a pair without follow-up comparison.
Begin by naming the experimental unit because apparent replication can come from repeated measurements of one batch rather than genuinely independent batches. Then decide whether observations are paired, how many groups are being compared and whether the response scale suits the proposed method.
Descriptive summaries and inferential conclusions have different jobs: the mean and SD describe the observed sample, while a test evaluates a null model under stated assumptions. P-values need a threshold and a precise scope, and practical importance still depends on effect size, uncertainty and the pharmaceutical question.
When assumptions fail, the repair may involve a different error model, transformation, robust procedure or redesigned experiment. The objective is not to find a software button that produces significance. It is to show why the analysis matches the way the data were generated and why the final sentence says no more than the evidence supports.
What this chapter covers
- 01
Experimental units and replication
- 02
Mean, SD and SEM
- 03
Normality and variance assumptions
- 04
Paired and unpaired comparisons
- 05
One-way ANOVA scope
- 06
P-value interpretation
- 07
Independent units and technical repeats
- 08
Global tests and pairwise follow-up
- 09
Effect magnitude beside statistical evidence
- 10
Captions that define uncertainty displays
Worked example · free
Interpret a global formulation comparison
- +2Identify more than two independent groups with reasonable parametric assumptions, so one-way ANOVA is appropriate.
- +1Conclude that the population means are not all equal at the stated threshold.
- +2Do not identify a specific pair until an adjusted follow-up comparison supports it.
Key terms
- Experimental Unit
- The independent object assigned to a treatment or condition.
- Technical Repeat
- Repeated measurement of the same experimental unit rather than a new independent observation.
- Standard Deviation
- The observed spread of values around their sample mean.
- Standard Error
- The estimated precision of a sample mean.
- One-Way ANOVA
- A global test of equality among several population means.
Statistical Decisions for Experimental Data FAQ
When should I use a paired comparison?
Use a paired method when each value in one condition has a meaningful match in the other, such as the same tablet measured before and after storage. Analyse within-pair changes and check their assumptions rather than treating all measurements as independent. Record what creates the pairing so the design remains visible.
Does a significant ANOVA identify the best group?
No. It supports the conclusion that the population means are not all equal. A prespecified or adjusted follow-up procedure is needed to identify supported pairwise differences, and practical importance still requires effect sizes and uncertainty. The largest sample mean is not automatically the best population value.
Why are SD and SEM not interchangeable?
SD describes variation among the observed values, while SEM describes precision of the estimated mean. Using SEM when the reader needs to see biological or manufacturing spread can hide meaningful variability. Label the interval explicitly in every figure and caption so its role cannot be mistaken.
Assessment move
For every practice dataset, write the experimental unit, pairing, group count, outcome type and assumptions before naming a test. Then state the null hypothesis in words and limit the conclusion to what that test can establish. Redraw published figures with error bars labelled as SD or SEM, and explain what each choice tells the reader.
Finish by practising global ANOVA conclusions that deliberately avoid naming a pair until follow-up evidence is supplied. Build a small decision tree from the source activities and test it on new laboratory scenarios. Change one feature at a time, such as turning independent groups into paired observations or adding another formulation, and explain why the method changes.
Keep a mistake ledger for false independence, unsupported pairwise claims, probability language about the null and confusion between spread and precision. For each error, write a corrected sentence that could be used under time pressure. Finally, practise a reporting paragraph that integrates the group summaries, uncertainty, global result and follow-up comparison without repeating the whole table.
That exercise joins statistical selection to the scientific writing expected elsewhere in the unit. Add a weekly assumption audit using a small invented dataset: predict what a diagnostic plot should look like, identify what departure would invalidate the planned test, and name a defensible response. Then rewrite one numerical finding for three audiences: a methods paragraph, a figure caption and a short-answer conclusion.
Compare the scope of each version and highlight where sample language must not become a population certainty. Use a timer for the final drill, but spend the review phase checking independence, units, error-bar meaning and the exact inferential boundary rather than merely checking arithmetic.
