← VCE Data Analytics U3O1

Limits and reliability of predictions

How much you can trust a prediction. It drops with small samples, outliers and predicting far beyond your data, so always state how uncertain the prediction is.

Part of: VCE Data Analytics - U3O1 - Data Analytics — Module 139, 9-10 Digital Technologies: Analysing and visualising data — Module 16, ACARA Digital Technologies Years 7–8 — Analysing and Visualising Data — Module 49, ACARA Digital Technologies Years 9–10 — Analysing and Visualising Data — Module 49

Understanding Limits and reliability of predictions in VCE Data Analytics U3O1

What it does: Giving a range shows how uncertain the prediction is, which is an honest way to report a prediction. The big change in slope shows a single outlier can distort the trend, so predictions based on it are less trustworthy. Small samples can be misleading. More data points give you more confidence in a trend. A bigger sample smooths out random variation, so predictions from it are more trustworthy. An outlier can pull a trendline off course. Check whether it is a mistake, and test the prediction with and without it. Predicting far beyond your data is risky. The further you extend the trendline, the less you can trust it.

Common mistakes: A small sample means low confidence, so the test should be n < 10. With n > 10 the rule flags large samples as low confidence, which is backwards. The outlier 300 drags the average up, but the median stays steady. It is the median that resists outliers, not the average.

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Learning
Duo
A student predicts next year's canteen sales using only 3 days of data. How reliable is the prediction?
Not very reliable, because the sample is too smallVery reliable, because any data makes a good prediction
Matches
Using 3 data points, I am 100% sure next year's result will be 52.
↓
A sample of 3 points is too small to be certain. The claim of 100% confidence ignores how unreliable small samples are.
Applying
Meanings
Term
reliability
Meaning
How much you can trust a prediction. It drops with small samples, outliers and predicting far beyond your data, so always state how uncertain the prediction is.
Practice
=COUNT(B2:B11)
Testing
Gaps
=(12,B2:B11,A2:A11)
Check Answer
Spots
1n ← COUNT(B2:B31)
2IF n > 10 THEN

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Quick Questions

1. A student predicts next year's canteen sales using only 3 days of data. How reliable is the prediction?
A. Not very reliable, because the sample is too small ✓
B. Very reliable, because any data makes a good prediction
Small samples can be misleading. More data points give you more confidence in a trend.
2. Which dataset gives a more reliable trendline for predicting test scores?
A. Scores from 200 students over 3 years ✓
B. Scores from 4 students on one day
A bigger sample smooths out random variation, so predictions from it are more trustworthy.
3. One student's data point is far above all the others and drags the trendline upward. What is it called, and what should you do?
A. An outlier: check it and see how much it changes the prediction ✓
B. A trend: ignore the other points and follow it
An outlier can pull a trendline off course. Check whether it is a mistake, and test the prediction with and without it.
4. Your data covers Years 1 to 5 of a school's enrolments. Which prediction is more reliable?
A. Predicting enrolments for Year 50
B. Predicting enrolments for Year 6 ✓
Predicting far beyond your data is risky. The further you extend the trendline, the less you can trust it.
5. Which statement about a prediction is better practice?
A. "Sales will be exactly 120. The trendline proves it."
B. "Sales will likely be about 120, but this is uncertain because we only have 6 months of data." ✓
Good data analysts state how uncertain a prediction is. A forecast is an estimate, not a guarantee.

Match the Pairs

=FORECAST(30, B2:B6, A2:A6) → A prediction made from only 5 data points, so it has low reliability and should be stated with caution
=FORECAST(100, B2:B20, A2:A20) → A prediction far beyond the data range (x values only go up to about 20), so confidence in it is low
Stating uncertainty: give a prediction as a range, not one exact number → Predicted sales: 120 (likely between 100 and 140)
Effect of an outlier: one extreme value can drag the trendline and make the prediction less reliable → Slope with outlier: 9.5 | Slope without: 2.1
Using 3 data points, I am 100% sure next year's result will be 52. → A sample of 3 points is too small to be certain. The claim of 100% confidence ignores how unreliable small samples are.
Data covers 2015-2020, so the trendline proves the 2060 population is exactly 8.4 million. → Predicting 40 years beyond the data is extrapolating too far, and 'exactly' ignores uncertainty.

Key Term

reliability
How much you can trust a prediction. It drops with small samples, outliers and predicting far beyond your data, so always state how uncertain the prediction is.

Fill in the Blanks

1. =FORECAST(12,B2:B11,A2:A11)
Hint: Type the function name that predicts a new y value from a trend in existing data.
2. =COUNT(B2:B6)
Hint: Type the function that counts how many data points you have. Few points means a small sample and a less reliable prediction.
3. IF samples < 10 THEN confidence ← "low"
Hint: Type the operator that means fewer than, to flag a small sample.
4. =MEDIAN(B2:B11)
Hint: Type the function that finds the middle value, which an outlier changes far less than the mean.
5. OUTPUT "Estimate only, not certain"
Hint: Type the pseudocode keyword that displays a message, so you can state how uncertain the prediction is.

Spot the Error

Question 1
A n ← COUNT(B2:B31)
B IF n > 10 THEN
C note ← "Low confidence"
D ELSE note ← "Fairly reliable"
Line B — A small sample means low confidence, so the test should be n < 10. With n > 10 the rule flags large samples as low confidence, which is backwards.
Question 2
A scores ← [52,55,58,54,300]
B avg ← AVERAGE(scores)
C med ← MEDIAN(scores)
D SAY "Average resists outliers"
Line D — The outlier 300 drags the average up, but the median stays steady. It is the median that resists outliers, not the average.
Question 3
A pred ← 412
B margin ← 30
C SAY "412 exactly, no doubt"
Line C — A prediction should state its uncertainty, for example 'give or take 30'. Claiming it is exact with no doubt overstates how reliable it is.
Question 4
A sample ← 4 students
B trend ← rises each week
C predict ← next week higher
D SAY "High confidence: tiny n"
Line D — A sample of only 4 is too small to trust a trend. The confidence should be low, not high.
Question 5
A x ← months 1 to 10
B y ← sales, one spike of 900
C Spike has no effect on trend
D Check the trend without it
Line C — An outlier can pull a trendline towards it and change the predictions. It should say the spike pulls the trendline up.

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