## ONE WAY ANOVA TEST WITH FOUR DIFFERENT TYPES OF CARS

### JAYA SHARMA

#### INTRODUCTION

Analysis of variance (ANOVA) is an inferential method used to test the equality of three or more population means.

H0: µ1= µ2= µ3= …=µk

This method is also referred to as single-factor ANOVA because we use a single property, or characteristic, for categorizing the populations. This characteristic is sometimes referred to as a treatment or factor. The objects of ANOVA are (1) estimate treatment means, and the differences of treatment means; (2) test hypotheses for statistical significance of comparisons of treatment means, where “treatment” or “factor” is the characteristic that distinguishes the populations.

#### OBJECTIVE

To compare four cars and calculate the f value by one-way Anova test

#### LITERATURE REVIEW

Analysis of variance (ANOVA) is a conceptually simple, powerful, and popular way to perform statistical testing on experiments that involve two or more groups. ANOVA is especially suited for experimental designs that involve pairing or blocking, repeated measures on the same subjects, or when looking to see if different factors in the experiment interact with each other. We discuss how the ANOVA works, review the most common types of ANOVAs, and discuss how to interpret the meaning of an ANOVA that achieves statistical significance. A positive ANOVA says that one or more groups are different from the others but does not specify which! Therefore, follow-up analyses must be carried out to identify which groups are significantly different. And, it is necessary to correct the resulting P-values to reflect the fact that multiple comparisons are being made. A variety of correction methods are discussed; each has advantages and disadvantages, and none is suitable for all experiments. (Neil R. Smalheiser MD, PHD, in Data Literacy, 2017)

Analysis of variance (ANOVA) is used to test for differences among three or more population means. It allows for multiple comparisons while holding the probability of a type I error (rejection of a true null hypothesis) at a preselected level. ANOVA works by comparing variance estimates: one due to chance factors alone and one due to chance plus treatment effect (if there is a treatment effect). ANOVA can also be used to study two or more treatment variables simultaneously. Although many researchers routinely use ANOVA in combination with post hoc comparisons to make all possible pair-wise comparisons, one should consider using planned comparisons in place of ANOVA if it is known in advance which comparisons are important to the study. (B.M. King, in International Encyclopaedia of Education (Third Edition), 2010)

#### DATA COLLECTION

The data is collected by the survey of 30 people on the four different cars by giving ratings from 1 to 10

Calculating f by using a one-way Anova tool in data analysis in excel.

#### DATA ANALYSIS

A = MG GLOSTER

B = HYUNDAI VERNA

C = BMW 3 SERIES

D = MARUTI SUZUKI BALENO

H0: A=B=C=D

H1: Anyone of them is different

• Calculated value in the excel sheet from Anova table, the F value is 1.35675

• Tabulated value from the f table 0.05, 3df, 116 df = 2.680

• As calculated f value (1,35675) is less than tabulated value. So, reject H0 and accept H1 which means any one of them is different.

#### CONCLUSION

ANOVA tests the null hypothesis that the population means are all equal. The alternative is that they are not all equal. This alternative could be true because all of the means are different or simply because one of them differs from the rest. So, from the above table I concluded that the tabulated F value is more than the calculated value, accept the alternate hypothesis and reject the null hypothesis.