BUSINFO700 Chap.6 Hypothesis Testing, Causality and Error Types
Hypothesis Testing, Causality and Error Types
This chapter covers the reasoning that sits underneath every bivariate test in the course. It begins with systematic error: the four conditions a relationship must meet before it can be called causal, namely variation together, no rival causes, the right time order and proximity, and why a very large dataset does nothing to remove confounding or reverse causation. It then turns to random error and hypothesis testing.
You will write null and alternative hypotheses, decide between one-tailed and two-tailed tests, and read a 5% threshold correctly. A two-by-two grid separates the sample conclusion from the population truth, defining Type I and Type II errors and showing why each test result leaves exactly one of them open.
The chapter ends with conclusions written in the order the practice test's bullets ask for: the result against the manager's expectation, bias and causality, and the error the analyst could have made, followed by the next step a manager should take.
What this chapter covers
- 01
Four conditions for causality
- 02
Confounding and systematic error in large datasets
- 03
Null and alternative hypotheses
- 04
One-tailed versus two-tailed tests
- 05
Type I and Type II errors
- 06
Writing a conclusion a manager can use
Worked example · free
Use the sample conclusion to name the possible Type I or Type II error
- 1Rule: the sample conclusion fixes the row. Support found leaves only a Type I error possible; no support found leaves only a Type II error possible.
- 1(a) p = 0.002 is below 0.05, so support was found for a difference: the only possible mistake is a Type I error, a difference that does not exist in the population.
- 1(b) p = 0.41 is above 0.05, so no support was found: the only possible mistake is a Type II error, a real effect of the price change that the sample missed.
- 1(c) p = 0.08 is above 0.05, so no support was found and a Type II error is possible; with only 24 users, random error is large, so that risk is real.
Key terms
- Alternative hypothesis
- H1, the claim of a difference or association that the analyst accepts as one explanation when H0 is rejected.
- Two-tailed test
- A significance test whose alternative allows a difference in either direction, used when theory does not predict the sign.
- Confounding variable
- A third factor linked to both the supposed cause and the effect, creating an association that is not causal.
- Concomitant variation
- The causality condition that cause and effect occur together or vary together as the hypothesis predicts.
- Significance level
- The threshold probability, normally 0.05, below which a test result leads to rejecting the null hypothesis.
Hypothesis Testing, Causality and Error Types FAQ
When should I use a one-tailed test instead of a two-tailed one?
Only when well-established theory predicts the direction of the effect before you see the data. In business intelligence work theories are usually weak and the opposite effect is often possible, so the Week 4 lecture recommends two-tailed tests as the default. A one-tailed test would leave no room to detect the unexpected direction.
Does a very large sample prove that a relationship is causal?
No. A large sample reduces random sampling error, so even tiny differences become significant, but it does nothing about systematic error. Confounding factors, wrong time order and selection effects remain however many rows the dataset has. Causality still needs the other three conditions to be argued.
How do I know which error the analyst could have made?
Look at the decision. If the test rejected the null hypothesis, the only possible mistake is a Type I error, a false positive. If it did not reject the null, the only possible mistake is a Type II error, a missed real effect. The practice test asks for exactly this reasoning.
What does a p-value of 0.03 actually mean?
The slides use a shorthand: below 5% means less than a 5% chance that the null is correct. Strictly, 0.03 means that if the null hypothesis were true, data at least as extreme as yours would turn up about 3% of the time. Either way the result is significant at 5%, but it is not a 97% chance that H1 is true.
Why might a surprising model result be wrong?
A counterintuitive coefficient may be a real discovery, but it can also come from coding errors, flawed data collection, a confounding variable or a misread output. The Week 4 lab shows a churn model with an unexpected positive age effect and asks students to investigate it with simple bivariate statistics first.
Assessment move
Learn the four causality conditions as a checklist you can write from memory in under a minute, then apply them to business claims you meet: who adopted the supposed cause, could they differ in other ways, and could the outcome have driven the cause instead? For hypothesis testing, practise writing H0 and H1 in words and in symbols for every scenario, and justify the tail in one sentence.
Draw the two-by-two error grid on scrap paper until it is automatic; the row is set by the test result, and the possible error follows. When reading output, cover the points the practice test's bullets ask for: the result compared with the manager's expectation, a comment on sample bias, a comment on causality, and the error type that remains possible.
An earlier test paper also asked about missing values, so add a line on them when the data have gaps. Time yourself against the suggested time beside each practice question.
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