# A REVIEW ON STUDENT t-TEST

**About Authors: ****Ram Chandra*, Abhimanyu, Dr. Ashutosh Aggarwal**

Seth G.L. Bihani S.D. College of Technical Education,

Institute of Pharmaceutical Sciences and Drug Research,

Sri Ganganagar, Rajasthan, INDIA**rcgedar@gmail.com*

**1. ****Introduction**

Biostatistics is contraction of biology and statistics, sometimes referred to as biometry or biometrics, is the application of statistics to a wide range of topics in biology. The science of biostatistics encompasses the design of biological experiments, especially in medicine and agriculture; the collection, summarization, and analysis of data from those experiments; and the interpretation of, and inference from, the results. Hypothesis testing determines the validity of the assumption with a view to choose between two conflicting hypotheses about the value of a population parameter. Hypothesis testing helps to decide on the basis of a sample data, whether a hypothesis about the population is likely to be true or false. Statisticians have developed several tests of hypotheses (also known as the tests of significance) for the purpose of testing of hypotheses which can be classified as:- (a) Parametric tests or standard tests of hypotheses, and (b) Non-parametric tests or distribution-free test of hypotheses. Parametric tests usually assume certain properties of the parent population from which we draw samples. Assumptions like observations come from a normal population, sample size is large, assumptions about the population parameters like mean, variance, etc., must hold good before parametric tests can be used. But there are situations when the researcher cannot or does not want to make such assumptions. In such situations we use statistical methods for testing hypotheses which are called non-parametric tests because such tests do not depend on any assumption about the parameters of the parent population. Besides, most non-parametric tests assume only nominal or ordinal data, whereas parametric tests require measurement equivalent to at least an interval scale. (Bolton Sanford 2004, Jakel James et.al. 2001)

**Reference Id: **PHARMATUTOR-ART-1546

**2. ****Student t- test**

Student t-test is based on t-distribution and is considered an appropriate test for judging the significance of a sample mean or for judging the significance of difference between the means of two samples in case of small sample(s) when population variance is not known (in which case we use variance of the sample as an estimate of the population variance). In case two samples are related, we usepaired t-test (or what is known as difference test) for judging the significance of the mean of difference between the two related samples. It can also be used for judging the significance of the coefficients of simple and partial correlations. The relevant test statistic, t, is calculated from the sample data and then compared with its probable value based ont-distribution (to be read from the table that gives probable values of t for different levels of significance for different degrees of freedom) at a specified level of significance for concerning degrees of freedom for accepting or rejecting the null hypothesis. It may be noted that t -test applies only in case of small sample(s) when population variance is unknown.

**2.1 Use of t-test**

In medical research, t-test is among the three or four most commonly use statistical tests. The purpose of a t-test is to compare the means of a continuous variable in two research samples in orders to determine whether or not the difference between the two observed means exceeds the difference that would be expected by chance from random samples. (Jakel James et.al 2001, Kothari C.R. 1990).

**2.2 Some important terms used in student t –test**

**(i) Degree of freedom-**

The term degree of freedom refers to the number of observations that are free to vary. The degrees of freedom for any tests are considered to be the total sample size minus 1 degree of freedom for each mean that is calculated. In the student’s t-test, 2 degree of freedom are lost because two means are calculated one mean for each group whose means are to be composed. The general formula for the degrees of freedom for the student’s two group t-test is N_{1} + N_{2 }– 2, where N_{1 }is the sample size in the first group and N_{2} is the sample size in the second group. (Jakel James et.al. 2001, Armstrong N et.al. 2006)

**(ii) The t-distribution**

The t-distribution was described by William Goasset, who used the pseudonym “student” when he wrote the description. The normal distribution is the z distribution. The t distribution looks similar to it, except that its tails are somewhat wider and its peak is slightly less high, depending on the sample size. The t-distribution is necessary because when sample size. The t distribution is necessary because when sample sizes are small, the observed estimates of mean and variance are subject to considerable error. The larger the sample size is the smaller the errors are and the more the t size distribution looks like the normal distribution. In the case of an infinite sample size, the two distributions are identical. For practical purposes, when the combined sample size of the two groups being compared is larger than 120, the difference between the normal distribution and the t distribution is negligible. (Jakel James et.al. 2001, Le Chap T 1992)

**2.3**** Technique to perform test**

1. Weneed to construct a null hypothesis - an expectation - which the experiment was designed to test. For example:- If we are analysing the heights of pine trees growing in two different locations, a suitable null hypothesis would be that there is no difference in height between the two locations. The student's t-test will tell us if the data are consistent with this or depart significantly from this expectation. So it is sensible to have a null hypothesis of "no difference" and then to see if the data depart from this.

2. List the data for sample (or treatment) 1.

3. List the data for sample (or treatment) 2.

4.Record the number (*n*) of replicates for each sample (the number of replicates for sample 1 being termed *n*_{1} and the number for sample 2 being termed *n*_{2})

12. A significant difference at p = 0.05 means that if the null hypothesis were correct (i.e. the samples or treatments do not differ) then we would expect to get a *t* value as great as this on less than 5% of occasions.So we can be reasonably confident that the samples/treatments do differ from one another, but we still have nearly a 5% chance of being wrong in reaching this conclusion.

Now compare your calculated *t *value with tabulated values for higher levels of significance (e.g. *p* = 0.01). These levels tell us the probability of our conclusion being correct. For example, if our calculated* t* value exceeds the tabulated value for *p *=0.01, then there is a 99% chance of the means being significantly different (and a 99.9% chance if the calculated t value exceeds the tabulated value for *p* = 0.001). By convention, we say that a difference between means at the 95% level is "significant", a difference at 99% level is "highly significant" and a difference at 99.9% level is "very highly significant".

Statistical tests allow us to make statements with a degree of precision, but cannot actually prove or disprove anything. A significant result at the 95% probability level tells us that our data are good enough to support a conclusion with 95% confidence (but there is a 1 in 20 chance of being wrong). In biological work weaccept this levelof significance as being reasonable. (Jakel James et.al. 2001, biology.ed.ac.uk )

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## Comments

vishal thakur (not verified)

Tue, 2013-01-15 16:57

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## biotechnology

can we use t test for simple experiments validation like production of enzyme in small level.

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