3. Inferential statistics
Study a sample
Conclude about the population
Two processes:
Estimation (Point or Interval)
Hypothesis testing

4. Objective of hypothesis testing
Detect differences between groups
Between men and women in taking alcohol
Between rural and urban in incomes
Detect associations between variables
Between smoking and lung cancer
Between birth weight and maternal height

5. Hypothesis testing Standard statistical procedure
Make judgment based on sample estimates to unknown population parameters

6. Null hypothesis (Ho) Relates to particular hypothesis under study
States, No relationship or difference
A hypothesis to be rejected or not

7. Alternative hypothesis (H1)
It disagrees with Ho
States, there is a relationship or difference

8. Note: Ho and H1 Both are concerned with the population
Statements referring to the population
Conclusions based on the sample
Possibility of errors (sampling errors)

9. Note: Ho and H1 You can never 100% sure Ho is true or not
Can ONLY say how likely the hypotheses are

10. Example
Is the familial aggregation of cardiovascular risk factors in general and lipid levels in particular.
Suppose we know that the average cholesterol level in children is 175 mg%/mL.
Identify a group of men who have died from heart disease within past year.
Measure the cholesterol levels of their offspring

11. Example
The average cholesterol level of these children is 175 mg%/mL (Ho)
The average cholesterol level of these children is not 175 mg%/mL (H1)
Note: Two-sided

12. Referring to the mean
Ho: μA = x-barB
H1: μA ≠ x-barB

13. Test statistics Measures used to reject or fail to reject the Ho
Examples: Z-test (SND), t-test, Chi-square test, etc

14. Type I and II errors Decision to reject Ho has errors
One may reject the ‘correct’ hypothesis

15. Type I and Type II errors
Decison: Ho
In reality
Ho is TRUE
Ho is FALSE
REJECT
Type I error
(α)
Correct desicion
(1 – β)
DO NOT
(1 – α)
Type II error
(β)

16. Example
Is the familial aggregation of cardiovascular risk factors in general and lipid levels in particular.
Suppose we know that the average cholesterol level in children is 175 mg%/ml.
Identify a group of men who have died from heart disease within past year.
Measure the cholesterol levels of their offspring

17. Example
What would be Type I error?

18. Example
The probability of deciding that the offspring of men who have died from heart disease have an average cholesterol not equal to 175 mg%/mL when if fact their average cholesterol level is 175
What would be Type II error?
The probability to decide that the offspring have normal cholesterol levels when in fact their cholesterol levels are not equal to 175 mg%/mL

19. Significance level English meaning ‘Important’
Here: ‘Probably true’ (not due to chance)
A finding may be true but NOT important
SL show how likely are results due to chance (consider results to be rare)

20. Significance level
Probability value small enough for you to reject the null hypothesis.
Normally set at 5%
Five percent chance of not being true
95% chance of being true IF YOU LOOKED AT THE ENTIRE POPULATION

21. Critical region/ value
The critical region of a hypothesis test is the set of all outcomes which, if they occur, cause the null hypothesis to be rejected and the alternative hypothesis accepted

22. Critical region/ value
The value of a test statistic at or beyond which we will reject Ho
A boundary that is “improbable” if the null hypothesis is true

23. Critical region/ value
The value of a test statistic at or beyond which we will reject Ho
A boundary that is “improbable” if the null hypothesis is true
Value of a test statistic at or beyond which we will reject Ho

25. p-value
The probability that the obtained results are due to chance IF Ho is true
This chance = Type I error
IF Ho is TRUE, it is a probability to obtain a test statstic value as or more extreme than the observed test statistic value

26. p-value Large p-values (p > 0.05) suggest Ho
Small p-values (p < 0.05) evidence for H1 (= vailability of difference, relationship)
p < 0.01 very strong evidence in favour of H1. There is a difference
In statistical software, indicated by “ Sig.”

27. Statistical tests
Mathematical formulae that produce p-values to allow investigators to assess the likelihood that chance accounts for the results observed in the study