1. Sumukh Deshpande n Lecturer College of Applied Medical Sciences
BIOSTATISTICS (BST 211)
Sumukh Deshpande n Lecturer College of Applied Medical Sciences
Lecture 10
Statistics = Skills for life.

2. The t-test Comparison of TWO means

3. Use of t-test … so far State H0 and H1 Conf. Int. with s UNKNOWN
Establish a
One tail or two tails?
Calc-t and read t-Crit
If Calc-t > t-Crit, Reject H0
Conf. Int. with s UNKNOWN
5-step Hypo Testing

4. Other Applications of t-test
Comparison of PAIRED population means.
Comparison of INDEPENDENT population means

5. Comparison of PAIRED means 1
Two related samples: before and after; with and without; …..
Chances are m1 ≠ m2
We test the following hypothesis:
"Is the observed difference sufficiently large to reject the Null Hypothesis?"

6. Comparison of PAIRED means 2
Example: examination scores for 10 students have been recorded before and after they participated in a revision.
Does this evidence suggest that the revision course had an effect on the performance of the students?

7. Comparison of PAIRED means 3
Step 1: Pair the data and calculate the differences (after – before) and their mean and sd.
Step 2: State H0 and H1
H0: md = 0
H1: md > 0
Xbard = 1.8
SDd = 3.293

8. Comparison of PAIRED means 4
Step 3: t or z? a? one or two tails?
Use t as n < 30 and one tail since H1: md > 0. a = 5%
Step 4: Calc-t
Step 5: Find t-crit
tn-1 = (1.8 – 0)/[3.293/√10]
Calc-t9 = 1.73
t-crit: t9 = 1.833
Therefore it seems that there is insufficient evidence to suggest that the revision course was effective.
If Calc-t > t-crit, Reject H < FAIL to reject H0

9. Comparison of PAIRED means 5
Step 3: t or z? a? one or two tails?
Use t as n < 30 and one tail since H1: md > 0. a = 5%
Step 4: Calc-t
Step 5: Find t-crit
tn-1 = (1.8 – 0)/[3.293/√10]
Calc-t9 = 1.73
t-crit: t9 = 1.833
If Calc-t > t-crit, Reject H < FAIL to reject H0

10. t-test for independent samples 1
samples are independent, not paired.
Ex: Gym A claims that their services are better than Gym B.
20 customers of A and 30 of B were asked for feedback (next Table).
Can we say that Gym A is right? Work at 95% CL.

11. t-test for independent samples 2
Step 1: Calculate the mean, the SD and the variance (S2) for each sample.

12. t-test for independent samples 3
Step 2: State H0 and H1.
H0: μA = μB
H1: μA > μB
both samples from the same population...
…Pooled Variance

13. t-test for independent samples 4
Step 3: is it z or t?. One tail or 2? a?
a = 5%, one tail t-test
Note: df is (n1+n2-2)
Step 4: Calc-t

14. t-test for independent samples 5
Step 5: Find t-Crit.
If Calc-t > t-Crit, Reject H0.
t-Crit(48 , 0.05)1 = 1.677
Since < 1.677, DO NOT reject the Null Hypothesis
The data presented, with 95% certainty, DOES NOT suggest that Gym A provides better services than Gym B.

15. Summary of comparison of 2 means
Paired
Independent
(Xaft – Xbef): Xbar, s
Xbar, s, s2 of each
State H0 and H1
z or t?. 1or 2 tails? a?
z or t?. 1or 2 tails? a?
Calc-t
t-Crit
If Calc-t > t-Crit, Reject H0