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.

The t-test Comparison of TWO means

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

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

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?"

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?

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

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 H0. 1.73 < 1.833. FAIL to reject H0

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 H0. 1.73 < 1.833. FAIL to reject H0

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.

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

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

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

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 1.209 < 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.

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