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Significance Testing Essentials
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1
Question
What are the objectives for learning about significance testing in this session?
Page 3
Answer
Understand the concept and relevance of hypothesis testing (significance testing); Define the 'null hypothesis' when comparing two groups; Be aware of the t-test (paired and unpaired) and its role in p-value testing; Understand the relationship between p-values and confidence interval testing.
2
Question
What are the four main stages of hypothesis testing?
Page 4
Answer
1. Define the null and alternative hypothesis under study. 2. Collect relevant data from a sample of individuals. 3. Calculate the value of the test statistic specific to the null hypothesis. 4. Compare the value of the test statistic to values from a known probability distribution. Interpret the p-value and results.
3
Question
What is the null hypothesis (H₀) in the context of a study?
Page 5
Answer
The null hypothesis is a precise statement about the population of interest, that there is no effect or no difference (usually the converse of the study hypothesis). It serves as the starting point of statistical analysis.
4
Question
Give an example of a study hypothesis and its corresponding null hypothesis involving FEV1 in young adults.
Page 5
Answer
Study hypothesis: FEV1 in young adults varies between males and females. Null hypothesis (H₀): The difference in mean FEV1 between the population of young adult males and females is 0 litres.
5
Question
Why can't we look at the whole population of young adult males and females in hypothesis testing?
Page 6
Answer
We use a sample to make inferences about the wider population. Is there any evidence from our sample against the null hypothesis?
6
Question
What is a test statistic in hypothesis testing?
Page 7
Answer
A test statistic assesses the evidence against the null hypothesis using the 'test statistic' calculated from our sample data. The type depends on the data (e.g., quantitative or categorical). It can then be 'looked up' in tables and a p-value obtained.
7
Question
What data type is suitable for the unpaired (2 sample) t-test?
Page 8
Answer
Quantitative (continuous) data, e.g., height, blood pressure, age, FEV1.
8
Question
What is the unpaired (2 sample) t-test used for?
Page 8
Answer
Comparing a continuous outcome (FEV1) between two groups (males versus females).
9
Question
What are the assumptions of the unpaired t-test?
Page 8
Answer
Assumes values follow normal distribution (in each of the two population subgroups - see lecture one). Assumes standard deviation the same in the population subgroups.
10
Question
In an example with FEV1 data, what were the sample sizes and means for males and females?
Page 9
Answer
Sample: 39 males, 46 females. Males: mean = 4.651, SD = 0.761. Females: mean = 3.311, SD = 0.657.
11
Question
What is the observed difference in mean FEV1 between males and females in the example?
Page 9
Answer
1.34 litres.
12
Question
In the FEV1 example, is the observed difference in mean FEV1 between males and females due to chance or a true difference?
Page 9
Answer
This is what hypothesis testing investigates.
13
Question
For the unpaired t-test in the FEV1 example, what is the difference in means?
Page 10
Answer
1.34 litres.
14
Question
What is the standard error (SE) of the difference in means for the FEV1 unpaired t-test example?
Page 10
Answer
0.156 litres.
15
Question
How is the test statistic calculated for the unpaired t-test in the FEV1 example?
Page 10
Answer
Test statistic = difference in means / SE of difference in means = 1.34 / 0.156 = 8.6.
16
Question
After calculating the test statistic for the unpaired t-test, what is the next step to derive the p-value?
Page 10
Answer
Look this up in appropriate statistical tables to derive the p-value.
17
Question
What is the p-value in hypothesis testing?
Page 11
Answer
P-value is a probability (ranges between zero and one). Smaller our p-value (obtained by looking up the appropriate test statistic in tables) LESS likely the observed results are due to chance. Stronger the evidence against the null hypothesis.
18
Question
How do we use the p-value to decide on the null hypothesis?
Page 11
Answer
Use p-value to decide whether to REJECT the null hypothesis.
19
Question
At what significance level is the decision often made to reject H₀ based on p-value?
Page 12
Answer
If p-value < 0.05 (5% significance level).
20
Question
What does a p-value less than 0.05 indicate?
Page 12
Answer
Less than 1 in 20 probability that observed results due to chance. Reject the null hypothesis (at the 5% significance level). Conclude that results reflect a difference or no effect in the population of interest.
21
Question
If p > 0.05, what do we conclude about the null hypothesis?
Page 13
Answer
Not enough evidence to reject the null hypothesis. Null hypothesis has not been proved correct! Do NOT say we accept the null hypothesis. We say: No evidence against the null hypothesis.
22
Question
In the FEV1 unpaired t-test example, what was the calculated test statistic?
Page 14
Answer
8.6.
23
Question
What p-value was obtained when looking up the test statistic of 8.6 in tables for the FEV1 example?
Page 14
Answer
p < 0.00001.
24
Question
What evidence does the p-value provide in the FEV1 unpaired t-test example?
Page 14
Answer
Strong evidence to reject (against) the null hypothesis. Less than 1 in 100,000 probability that observed difference (1.34 litres) is due to chance.
25
Question
From the p-value in the FEV1 example, what do we say about the null hypothesis?
Page 15
Answer
If the null hypothesis were true, there is less than 1 in 100,000 probability that the difference we have seen between sample means occurred by chance. We reject the null hypothesis and say the difference is significant at the 0.001% significance level.
26
Question
What does the conclusion from the FEV1 example indicate about the population?
Page 15
Answer
Difference reflects a true difference in FEV1 between the population of young adult males and females.
27
Question
In the FEV1 confidence interval example, what is the observed difference in mean FEV1?
Page 16
Answer
1.34 litres (also calculated 95% S.E. = 0.156 litres).
28
Question
How do we calculate a 95% confidence interval for the difference in means in the FEV1 example?
Page 16
Answer
Can calculate a 95% confidence interval for this difference in means.
29
Question
What is the formula for the 95% CI for difference in means?
Page 17
Answer
Difference in mean ± (1.96 × SE of difference).
30
Question
Calculate the 95% CI for the difference in means in the FEV1 example.
Page 17
Answer
1.34 ± (1.96 × 0.156) = 1.34 ± 0.306 = (1.034 litres, 1.646 litres).