A group tested for a drug shows 60% improvement as against a standard group showing 40% improvement. The best test to test the significance of result is -
Ans. is 'b' i.e., Chi-square test Chi square test o Is used when the observation are in the form of propoions (for qualitative data) o The outcome are in clear cut answers; yes or no. As in the example the HBsAg is either present or not present. In contrast when the observation is normally distributed in the population e.g blood pressure, blood sugar ; student test is used. o In the example comparing the occurence of hepatitis B surface antigen in medical and dental students, use of chi square analysis is appropriate because the outcome variables are dichomatous. Students are classified by the presence or absence of HBsAg. Student t test o is used when the outcome variable is normally distributed in population (for quantitative data) e.g blood pressure, blood glucose. In the example student t test is used to assess the difference between mean systolic pressure of pregnant and non pregnant women ( to know the effect of pregnancy on mean systolic blood pressure) because mean systolic blood pressure is normally distributed in the population. Every single lady has a mean systolic blood pressure. It may be low or high , but she has a value of mean systolic blood pressure. Students t test may be following types: i) Unpaired t test (Independent t test) : It compares the mean of two small samples: The data is unpaired from two independent sample. for example, blood sugar concentration is measured in two different group (A group of 10 patients and other group of 8 patient). To test the significance of difference between the means of the two groups, unpaired t test is used. ii) Paired t test : It compares the mean in paired data, before and after the intervention from same sample. For example, Blood sugar level in a sample of 10 patients is measure before giving and after giving the oral hypoglycemic. In this condition paired t test is used. Chi-square test Vs Student t test In the example student t test is used to assess the difference between mean systolic pressure of pregnant and non pregnant women ( to know the effect of pregnancy on mean systolic blood pressure) because mean systolic blood pressure is normally distributed in the population. Every single lady has a mean systolic blood pressure. It may be low or high , but she has a value of mean systolic blood pressure. o But suppose we change the example in a way that we make a clear cut definition of hypeension ( such as mean systolic blood pressure over 140 mm of Hg will be taken to be hypeension) and then look for hypeension among pregnant and non-pregnant women. o The test now used to analyse the outcome will be chi square test since the outcomes are now in the form of dichomatous data i.e yes or no (a woman is either hypeensive or not hypeensive. This is in contrast to mean systolic blood pressure which was normally distributed among ladies; every lady had one value of mean systolic blood pressure). Analysis of Variance (ANOVA) (F test/ F ratio) o ANOVA is considered as an extension of the student t test for the significance of the difference between two sample means. The student t test can be used only for making just one comparison (between two sample means), or between a sample mean and hypothesized population mean. ANOVA is used when more than one comparison is to be made (When means of more than two groups are being compared). o For example, BP is measured in more than two groups of men (married, unmarried, widowed, separated and divorced). In this situation ANOVA test is best. Fisher's test (Fisher's exact test) o It is same as Chi square test; the difference being in sample size which is small for Fishers' t test; (i) When sample size is big, chi square test is used. (ii) When sample size is small fisher test is used. The chi-square test is acceptable when all the expected cell values are greater than 1 and no more the 20% of cells have expected value below 5. Otherwise fisher's exact test is recommended. o For example, a study is under taken to determine whether smoking is associated with chronic bronchitis and the observed frequencies are:- Chronic bronchitis No bronchitis Smoking 6 4 10 No Smoking 2 7 9 8 11 l9 o Now we will figure the expected frequencies :- There are all together 8 chronic bronchitis patients among 19 person examined (a propoion of 8/19); and 11 persons out of 19 have no chronic bronchitis (a propoion of 11/19). The expected frequency will be:- Expected frequency of chronic bronchitis in smokers = Total number of smokers (10) x propoion of persons having chronic bronchitis (8/19) = 4.2 Expect frequency of smokers not developing bronchitis = Total number of smokers (10) x propoion of person not developing bronchitis (11/19) = 5.7. Expected frequency of chronic bronchitis in nonsmokers = Total number of non-smokers (9) x propoion of persons having bronchitis (8/19) = 3.7 Expected frequency of nonsmoker not developing branchitis = total number of non-smoker (9) x propoion of person not developing brachitic (11/19) = 5.2. Chronic Bronchitis No Bronchitis Smoking 10 (8/19)= 4.2 10 (11/19)=5.7 No Smoking 9 (8/19)= 3.7 9 (11/19) = 5.2 Because, 50% of cells (2 out of 4) have an expected frequency less then 5, fisher exact test should be used not chi-square test. Z-test o Z-test is a variant of student t test. It involves the same steps as t-test and can be used when the sample is large enough (n > 100) for the standard detion to provide a reliable estimate of standard error. Mc Nemar test: It is used for paired dichomatous data i.e. it is similar to paired t test, the difference being that paired t test is used for variable which is normally distributed in population such as mean systolic B.P., Serum sodium Concentration where as Mc Nemar test is used when the data are in dichomatous form (i.e. yes & no -either the person is hypeensive or non hypeensive, either he is diseased or not diseased). Wilcoxon Rank-Sum test (mann-whitiney 'II' test) o It is non parametric equalent of the unpaired t tests. Similar to unpaired t test it is used when data is unpaired from two independent sample. However, it is used for qualitative data (as all non-parametric tests) ---> compares the percentage, fractions and propoions in two unpaired samples. Wilcoxon Signed - Rank Test o It is nonparametric equalent ofpaired t test. It is used when data (qualitative) is paired (before and after intervention) from the same group --> compares the percentage, fractions and propoions in two paired samples. Sign-test Sign test is also non-parametric equalent to paired t test and is very much like wilcoxon signed ranked test. However, instead of determining the ranks of the absolute difference we just keep track of the number of positive or negative differences. o That means, both wilcoxon signed ranked test and sign test compare percentage, propoions and fractions in pair data. However, Wilcoxon signed rank test determines the ranks of the absolute differences and sign test keeps track the number of positive and/or negative differences.
Student T test
Chi square test
Paired T test
Test for variance