LEC 4 Parametric Tests l

Question 1

Considerations when comparing data between/among groups (4)

Answer 1

1. Number of goups
2. Independent or paired/related groups?
3. Data is nominal, ordinal or continuous?
   - continuous -> normal or non-normal?
4. Assumptions for each test

Question 2

Comparing 2 groups with continuous (normally distributed data)
- paired/related group

Answer 2

Paired sample t-test

Question 3

Procedure for hypothesis testing (6)

Answer 3

1. Define the problem
2. State the hull and alternative hypothesis
3. Compute test statistic
4. Find p-value for the computed test statistic
5. Compare p-value with given significance level
   (alpha = 0.05)
6. State conclusion
   - reject null hypothesis : there is significance difference
   - fail to reject null hypothesis : no significance difference

Question 4

Parametric tests assumptions (2)

Answer 4

1. Underlying distributions of samples are normal

2. Variances are the same (equal variance)

Question 5

Paired sample t-tests assumptions (3)

Answer 5

1. Difference in values are normal distribution
2. Random samples are drawn from population
3. Two underlying populations are paired

Question 6

Paired sample t-test hypothesis

Answer 6

Null hypothesis : Population mean difference (Ud) = 0

Alternate hypothesis : Population mean difference (Ud) =/ 0

Question 7

Types of pairing in Paired Sample t-tests

Answer 7

1. Self-pairing
   eg same patient undergo 2 types of treatment at diff periods
2. Matching
   eg match patients with similar characteristics. 1 undergo treatment A while the other undergo treatment B

Question 8

Two-tailed test or one-tailed test

Answer 8

Two-tailed test

• qn is ANY difference
• p-value x 2 (if graph is symmetrical eg t-test)

One-tailed test
- qn is A>B or B>A

Question 9

Normality test

Answer 9

Test for the distribution of data to be normal or not normal
n<50 : Shapiro-Wilk
n>=50 : Kolmogorov-Smirnov

Question 10

Normality test hypothesis

Answer 10

Null hypothesis : data distribution is normal

Alternate hypothesis : data distribution is not normal

Question 11

Independent sample t-tests assumptions (4)

Answer 11

1. The samples are random samples of their population
2. Two underlying population is normally distributed
3. Two underlying population is independent
4. Two underlying population have equal variances

Question 12

Tests for variance equality (2)

Answer 12

1. F test
   - normal distribution of populations
   - 2 populations
   F = ratio (larger variance/smaller variance)
2. Levene’s test
   - normal / non-normal distribution
   - >=2 populations

Question 13

Is there a unique F distribution graph?

Answer 13

No.

It is a family of F distribution. 1 F distribution for each pair of degree of freedom (df1 & df2)

Question 14

F distribution graph

Answer 14

• positively skewed (right skewed)

- non-negative values

Question 15

Independent sample t-tests with EQUAL variance hypothesis

Answer 15

Null hypothesis : No difference in mean

Alternate hypothesis : There is difference in mean

Question 16

Independent sample t-tests with UNEQUAL variance hypothesis

Answer 16

Null hypothesis : No difference in mean

Alternate hypothesis : There is difference in mean

Question 17

F test hypothesis

Answer 17

Null hypothesis : population variance are equal

Alternate hypothesis : population variance are not equal

Question 18

t-test distribution graph

Answer 18

• symmetrical

- if two-tailed, multiply p-value by 2

Question 19

Comparing 2 groups with continuous (normally distributed data)
- independent group

Answer 19

Independent sample t-test

• equal variance
• unequal variance