Comparing means Norhafizah Ab Manan

After class, you should Understand independent t test, paired t test and ANOVA Know how to calculate the t statistics Find the t tabulated from t distribution table

Comparing two means How can we get a mean? What data?- categorical or numerical?

Independent t test Is cholesterol level differ between male and female students? What is the null hypothesis for this study? malefemale

Independent t test Measure – Compare two means Assumptions 1.In each group of the dependent variables, the distribution is normal 2.Random sample How to test the assumption?

Steps in hypothesis testing 1.Define the null and alternative hypothesis  H o =The population means in two groups are equal  H a =The population means in the groups are not equal 2.Calculate the t statistics/ t calculated 3.Compare the t statistics to the value from t-distribution 4.Interpret the results

Example; A researcher interested to compare cholesterol level between male and female students. There are 12 males and 7 females. The data was: GroupSample size Mean (mmol/L) SD (mmol/L) Male Female

1. Define null and alternative hypothesis. Ho= The cholesterol means in male and female students are equal Ha= The cholesterol means in male and female students are not equal

2. Calculate the t statistics

GroupSample size Mean (mmol/L) Variance (mmol/L) Male Female = 0.483

2. Calculate the t statistics GroupSample size Mean (mmol/L) SD (mmol/L) Male Female = 0.778/0.3305=2.36

3. Compare the t statistics to the value from t-distribution If t calculated > t tabulated (from table)- we reject the null hypothesis If t calculated < t tabulated (from table) – we fail to reject the null hypothesis

One tailed Right-tailed Sign of Ha is > Key word: More than Left-tailed Sign of Ha is < Key word: Less than Rejection area

Two tailed The sign of H A is ≠ Key word: no different Rejection area

3. Compare the t statistics to the value from t-distribution Find the t tabulated from t distribution table =2.45 (from table) with alpha error= 95%, Upper tailed = 2.5%. Degree of freedom= the smaller of (n 1 -1) or (n 2 -1) 6? T statistics=2.36 2,45 -2,45 0

4. Interpret the results The t calculated value is in the critical region Reject the null hypothesis There is different of cholesterol between gender

Paired t test Measure – Compare two dependent means (before and after) Assumptions 1.Distribution of the different is normal 2.Random sample How to test the assumption?

Example A researcher interested to determine the effectiveness of an intervention towards BP. The BP of the subjects were measured twice; before and after the intervention. MeasureSample size Mean of dSdSd Pre-interV

1. Define null and alternative hypothesis. Ho= there is no different of BP before and after the intervention Ha= there is a different before and after the intervention

2. Calculate the t statistics The formula for t statistics: t=test statistics ḋ = mean of the difference S d =Sd of the difference n= sample size

2. Calculate the t statistics MeasureSample size Mean of dSdSd Pre-interV =2.930 Note: A hypothesized mean difference ( μ d ) can be any specified value. The most common value specified is zero.

3. Compare the t statistics to the value from t-distribution T calculated= T tabulated with df (14) and alpha(0.05)= 2.14

4. Interpret the results The t calculated value is in the critical region Reject the null hypothesis There is a different between before and after the intervention

ANOVA To compare means between more than two groups Variable: – Independent variable: Categorical – Dependent variable: Numerical Assumptions: – Data is normal distributed – Equal variance

Examples To determine whether BMI is different between age groups or not To study the effect of 3 different types of anti hypertensive drug on 120 patients. To compare the mean different of IQ scores among 3 classes

References Basic Biostatistics statistics for public health practice B Burt Genstman. Jones and Batlett Publisher Inc. Medical statistics at a glance. 3 rd Edition Aviva Petrie & Caroline Sabin. Wiley-Blackwell.