**Introduction:**

**The conventional t-test allows a researcher to compare between the means of two populations. ANOVA or “ANALYSIS OF VARIANCE” provides the researcher with an opportunity to compare between more than two population means. The terminology is ANOVA or “ANALYSIS OF VARIANCE” because in this type of analysis the variances are mainly analyzed in order to compare the mean between three more than three populations.**

**Logic Behind The Concept Of ANOVA:**

**The purpose of ANOVA is to compare the means between three or more than three populations to check the statistical significance. However this is done by analyzing the variance. The total variance is divided into components; one which is due to the differences between the means and the other component that is due to random errors. First one is between group variance and the latter is within group variance. The between group variance is tested for statistical significance and if tested significant then the null hypothesis of equality between means is rejected and the alternative hypothesis is accepted. Since the analysis includes the study of variance hence the test is known as Analysis Of Variance or ANOVA.**

** Why ANOVA…Why Not Multiple “t tests”?**

**A student may argue for more than 2 populations we can do multiple “t tests”, taking two populations at a time. This method, though feasible will give arise to the probability of Type I error. Here is the explanation:**

**We know Type I error is rejecting when the null hypothesis is true. Let us take the level of significance (α) be .05, thus the probability of not achieving a statistically significant result is 1-0.5 i.e. .95.**

**Thus for two t tests the probability will be 1-(.95) ^{2} i.e. .0975.**

**So we see there is a rise in probability of committing Type I error from .05 to .0975 when the number of “t test” increases from one to two.**

**Similarly if there are 4 populations then no of “t test” to be performed is 6.**

**Thus the probability of committing Type I error will be 1-(.95) ^{6} i.e. .265 which is greater than 1 out of 4 probability.**

**So we observe that with the increase in performing multiple “t tests” the probability of committing Type I error also increases.**

**Hence it is not advisable to perform “t test” when the number of population is more than 2.**

**However ANOVA compares the means of all the populations simultaneously and at the same type keeps the probability of committing Type I error at the designated level.**

**Hence for more than 2 populations ANOVA is performed and not the “t test”.**

**Next: Types and Assumptions of ANOVA**