A small difference between two averages is weak evidence when the readings within each group vary by more than that difference. Compare the gap with the spread before choosing your words.
This lesson follows identifying the comparison group and belongs to the set on evaluating a science claim from a supplied dataset.
What is the spread check?
- Work out the average of each group.
- Find the range of each group: highest minus lowest.
- Compare the gap between the averages with the ranges.
If the gap is much smaller than the ranges, the groups overlap heavily and the difference may be chance.
Worked example 1: a gap lost in the spread
An original test grows 5 plants with food (Group P) and 5 without (Group Q). Heights after 14 days, in cm:
| Group | Readings | Total | Average | Range |
|---|---|---|---|---|
| P (food) | 16, 18, 19, 17, 20 | 90 | 18 | 20 − 16 = 4 |
| Q (water) | 14, 19, 16, 20, 16 | 85 | 17 | 20 − 14 = 6 |
Step 1: averages. P: 90 ÷ 5 = 18 cm. Q: 85 ÷ 5 = 17 cm. The gap is 18 − 17 = 1 cm.
Step 2: ranges. P covers 16 to 20 cm and Q covers 14 to 20 cm. The ranges overlap from 16 to 20 cm.
Step 3: compare. The 1 cm gap is much smaller than the 4 to 6 cm spread inside the groups. Some plants in Q (19 and 20 cm) were taller than most in P.
Conclusion. The average height was 1 cm higher with plant food, but the readings overlap heavily, so the data gives only weak support that plant food increased height. More plants would help.
Worked example 2: a clear gap
Now suppose Group R had heights 22, 23, 24, 23, 23 (total 115, average 23, range 2) and Group Q is as before (average 17, range 6).
The gap is 23 − 17 = 6 cm. The readings for R (22 to 24 cm) do not overlap the readings for Q (14 to 20 cm), so the difference is clear. Even here the conclusion is limited to the conditions tested.
The mistake that costs marks
The slip is to call any difference proof. “Group P is taller, so plant food works” ignores the overlap.
| Wrong | Right |
|---|---|
| “Plant food clearly works” | “The average was 1 cm higher, but the readings overlap” |
| “There is no difference” | “The difference is small compared with the spread, so the support is weak” |
| “The groups are the same” | “The data cannot show a difference with this few plants” |
The repair is to report the gap and the overlap in the same sentence.
Check yourself
Two fictional groups of 5 students did a reaction-time test, in seconds. Group A: 0.25, 0.30, 0.28, 0.27, 0.30.
Group B: 0.29, 0.26, 0.31, 0.30, 0.29. A student says Group A reacts faster. Comment on this.
Answer
Group A total: 0.25 + 0.30 + 0.28 + 0.27 + 0.30 = 1.40, so the average is 1.40 ÷ 5 = 0.28 s. Group B total: 0.29 + 0.26 + 0.31 + 0.30 + 0.29 = 1.45, so the average is 0.29 s.
The gap is 0.01 s. The ranges are 0.30 − 0.25 = 0.05 s for A and 0.31 − 0.26 = 0.05 s for B, and they overlap from 0.26 to 0.30 s.
The gap is much smaller than the spread, so the data gives only weak support that A reacts faster.
What to study next
Go on to separating a repeated result from a fair-test design, which shows why agreeing repeats can still be unfair. The graph evidence and fair-comparison lab provides datasets to practise on.
To practise the spread check with a teacher, see online one-to-one Science tuition.