Lecture 7 Hypothesis Testing in Biostate.pptx
- 1. Hypothesis Testing Muhammad Aurangzeb (BSN,MPH,MSN*) Lecturer(INS-KMU)
- 4. 4 Hypothesis Testing • Statistical inference that allows one to test any desire claim about a population characteristics/ parameter by using information from study sample. • Allows us to use sample data to test a claim about a population, such as testing whether a population mean equals some number.
- 5. Examples • Does mean creatinine level of patients receiving a particular antibiotic is different from mean creatinine level of the general population ? • Does the NURSING students spend more than 6 hours in Library studying Biostatistics per week?
- 6. 6 What is test of hypothesis? Sample(s) Population(s) Selected at random Population(s) Population(s) Sample statistic Statistical test results Statistical Inference • It tests whether a population parameter is less than, greater than, or equal to a specified value (hypothetical).
- 13. 13 Underlying assumptions for testing of hypothesis for population mean • The sample has been randomly selected from the population. • The underlying population is normally distributed (or if not normally distributed, then n is large say greater than or equal to 30). • Population variance (2 ) either known or sample variance (s2 ) assumed to be approximately equal to population variance (2 ), when n is large.
- 14. 14 Basic Elements of Testing Hypothesis Step-I Statement of hypothesis Null Hypothesis Alternative Hypothesis (Researcher Hypothesis) Step-II Choice of appropriate level of significance () or One tailed or two tailed Step-III Rejection Region (Critical Region): Based on alternative hypothesis and level of significance (). Step-IV Test Statistic (Formula): Application of sample results in the formula to calculate the value of test statistic use for decision purpose. Step-V Conclusion: If the calculated value of the test statistic falls in the rejection region, reject H0 in favor of Ha, otherwise fail to reject H0 .
- 15. 15 Steps in a Hypothesis Test 0 0 0 : : a H H 0 0 0 : : a H H 0 0 0 : : a H H Step 1 Write down the appropriate null (H0) and alternative (Ha) hypotheses. (Write H0 and Ha as mathematical statements
- 16. 16 Steps in a Hypothesis Test (Contd.) Step 2: State the level of significance Note: Apply the same level of significance () used at the time of sample size determination.
- 17. 17 Steps in a Hypothesis Test (Contd.) Step 4: Determine the critical region using Z- table The critical region is also known as Rejection region. When the computed test statistic falls in the rejection region we reject the null hypothesis in favor of the alternative hypothesis
- 25. Steps in a Hypothesis Test (Contd.) • Step 4: Find the test Statistic • Perform the calculations to compute test statistic (Z-score) • Test statistic: 25 n x z 0
- 31. 31 Example: Mean APTT among DVT patients • A random sample of 30 hospitalized patients suffering from DVT had a mean APTT of 50 seconds. If the mean APTT of general population (patients) is 53 seconds with a standard deviation of 7 seconds then using a 5 percent level of significance test if the mean APTT in this group is different from that of general population. – Does the data provide sufficient evidence to conclude that mean APTT for DVT patients is different from 53 seconds? Let = Mean APTT of all hospitalized DVT patients. (True/Actual)
- 32. 32 Hypothesis Description Step 1: Stating null & alternative hypothesis Ho : =53 seconds The mean APTT of DVT patients is equal to 53 seconds. Ha : ≠53 seconds The mean APTT of DVT patients is different from 53 seconds. Step 2: Level of significance (α) = 0.05 Step 3: Test Statistic 35 . 2 28 . 1 3 30 7 53 50 7 ; 53 50 ; 30 0 Z x n Example: Mean APTT among DVT patients (Contd.) n x z 0
- 33. 33 Table Value: Þ 0.5 – 0.025 = 0.4750 ÞZα/2= ±1.96 (Critical Value) Significance Level: α = 0.05 α/2=0.05/2=0.025 (Area above or below Critical Value) 0 0.1 0.2 0.3 0.4 0.5 -3 -2 -1 0 1 2 3 z Area above Z
- 34. 34 Step 4: Critical Region Reject Ho if Z cal > Z tab or Z cal < -Z tab -2.35 Example: Mean APTT among DVT patients (Contd.) -1.96 1.96 0.025 0.025
- 35. 35 Step 5: Conclusion Since the calculated value of the test statistic (Zcal=-2.35) falls in the rejection region, so, we are rejecting our null hypothesis at 5% level of significance and we have sufficient evidence to conclude that mean APTT of DVT patients is different from 53 seconds.
- 37. Tutorial • Suppose the chest circumference of new born female babies is normally distributed with a mean of 35 c.m.and S.D. of 2 c.m.A sample of 50 baby girls from a remote area of Khyber agency are found to have a chest circumference of 32.5 c.m. Is the chest circumference of these babies less than the whole population? Test at significance level = 0.05