# A REVIEW ON STUDENT t-TEST

Example1. The Table shows gain in body weight of two lots of young rats (28-80 day old) mentained on tw0 different diets (high and low protein). Calculate whether the change in the body weight observed is due to diet or not.

 S. No Group 1 (high protein) S. No Group 2 (low protein) 1 134 1 70 2 146 2 118 3 104 3 101 4 119 4 85 5 124 5 107 6 161 6 132 7 107 7 94 8 83 9 113 10 129 11 97 12 123

n1 =  12

for t = 1.89 at 17 degree of freedom p > 0.05. Hence, the observed difference, gain in body weight due to two different types of diets is not significant. (Kulkarni S.K, 1999)

2.4 Typesof student t-test
There are two type ofstudent t-test-
(i)                 One -tailed test
(ii)               Two-tailed test

The two-tailed test is generallyrecommended, because differencein either direction are usually importantto document. For example, it is obviously important to know ifa new treatment is significantly betterthan a standard or placebo treatment, butit is also important to know if a new treatment issignificantly worse and shouldtherefore be avoided.In this situation, the two-tailedtest provides an accepted criterion forwhen a difference shows thenew treatment to be either better or worse.

Sometimes, only a one-tailed test is needed. For example, that a new therapy is known to cost muchmore than the currently used therapy. Obviously, it would not be used if it were than the current therapy. Under these conditions, it acceptable to use a one- tailed test. When this occurs, the 5%rejection region for the null hypothesis is all put on one tail distribution, instead of being evenly divided between the extreme of the two tails.

In the one tailed test, the null hypothesis non rejection regionextends only to 1.645 standard errors above the ‘no difference’ point of 0. In the twotailed test, it extends to 1.96 standard errorsabove and below the ‘no difference’ point. This makes the one tailed test more robust-more able to detect a significant difference, if it is in the expected direction. (Jakel James et.al. 2001, Kothari C.R.1990)

2.5     Paired t-test
In many medical studies, individuals are followed over time to see if there is a change in the value of some continuous variable. Typically, this occurs in a “before and after”  experiment, such as one testing to see if there was a drop in average blood pressure following treatment or to see if there was a drop in weight following the use of a special diet. In this type of comparison, an individual patient serves as his or her own control. This appropriate statistical test for this kind of data is the paired t-test. The paired is more robust than student’s t-test because it considers the variation from only one group of people, whereas the student’s t-test considers variation from two groups. Any variation that is detected in the paired t-test is attributable to the intervention or to changes over time in the same person.

2.6 Calculation of the value of t
to calculate a paired t-test, a new variable is crated. This variable, called d, is the difference between the value before and after the intervention for each individual studied. The paired t-test is a test of the null hypothesis that, on the average, the difference is equal to 0, which is what be expected if there were no change over time. Using the symbol d? to indicate the mean observed difference between the before and after values, the formula for the paired t-test is as follows:

Degree of freedom df = N-1

The formula for the student’s t-test and the paired t-test are similer. The ratio of a difference to the variation around that difference (the standard error). In the student’s t-test, each of the two distribution to be compared contributers to the variation of the difference, and the two variance must be added. But in the paired t-test, there is only one frequency distribution, that of the before and after difference in each person. In the paired t-test, because only one mean is calculated (d?), only 1 degree of freedom is lost, therefore the formula for degree of freedom is N-1.

2.7 Interpretation of the results-
the value of t and their relationship to p are shown in a statistical table in the appendix. If the value of t is large, the p value will be small, because it is unlikely that is large t ratio will be obtained by chance alone. If the p value is 0.05 or less, it it is customary to assume that there is a real difference.(Jakel James et.al. 2001, Lachman Leon et.al. 1990)

References
1.    Armstrong N. Anthony, James Kenneth C, “Pharmaceutical Experimental Design and Interpretation” 2006, Published by Taylor & Francis Ltd, London, Page no.14-16
2.    Bolten Sanford, “pharmaceutical Stastics” Practical and clinical applications, Third edition, 2004, Published by Marcel Dekker Inc., New York, Page no 265 267,273
3.    Jekel James F, et al., “Epidemiology, Biostatistics, and Preventive Medicine” Second edition 2001, Published by Saunders Publishers, Pennsylvania, Page no.160-163
4.    Kothari C.R, “Research Methodology Method & Techniques” Second edition 1990, Published by New Age International Publishers, New Delhi, Page no.184, 195-196, 256-259
5.    Kulkarni S.k, “Handbook of Experimental Pharmacology”, Third edition 1999, Published by Vallabh Prakashan, Delhi, Page no.175 -17
6.    Lachman Leon, Lieberman Herbert, Kanig Joseph L, “The Theory and Practice of Industrial Pharmacy” Third edition 1990, Published by Varghese Publishing house, Dadar Bombey, Page no.269
7.    Le Chap T, “Fundamental of Biostatistical Inference” Volume 124, 1992, Published by Marcel Dekker Inc, New York, Page no. 220-222
8.    Student’s t-test procedure, biology.ed.ac.uk/research/groups/jdeacon/statistics/tress4a.html [accessed on 10 Aug.2012]

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