Question

Please use an example to discuss the Analysis of Variance. Please discuss why some experts believe it should be called “Analysis of Means.”

Note: The response should be a minimum of 350 words typed please and thank you!

Answer 1

Analysis of variance is a statistical tool used in statistics. It splits the observed aggregate variability found in a data set into two parts i.e. systematic factors and random factors. The systematic factors have a statistical influence on the data set while the random factors do not.

An example is as follows: We have three medical treatments for patients having a similar disease. One option is to select the cure which takes the least amount of time is the best amongst them. The question is what if a patient is already partially cured, or of any other medication is working effectively. To make a confident and reliable decision, we will use analysis of variance (ANOVA).

We can analyze the time each of the three treatments took to cure the patients. We can use a statistical method to find out how different each treatment is from the other and compare the three samples. The technique which compares the samples based on their mean is called ANOVA

ANOVA:

We take the example of a study, which wants to understand the impact of music on the students' concentration levels in the class.

One way ANOVA

Ten students from three classrooms were randomly selected of similar age group. The different environment was created in each classroom. Classroom A had music playing constantly. Classroom B had music playing variably. Classroom C had no music.

Classroom	Test Scores										Mean
A	7	9	5	8	6	8	6	10	7	4	7
B	4	3	6	2	7	5	5	4	1	3	4
C	6	1	3	5	3	4	6	5	7	2	4.3
										Grand mean	5.1

It shows a mean score of group A is better than the average mean secure.

Two-Way ANOVA

We learn the impact of music on a group of students of similar age group. In case we need to understand the impact of music on people of different age groups or the impact of a different teacher. In this case, the outcome is dependent on two variables so it is known as two way ANOVA. One way Anova showed that variable music and no music showed almost the same mean. Hence, variable music seems to have no impact on the performance or the scores of the student. Therefore, we will omit the variable music in two way ANOVA and introduce a new variable age factor. The two-factor analysis will define if age group and the impact of music on the performance of students in different age groups (4-8 yrs, 8-13 yrs, 13-17 yrs) with music without music. Two-way ANOVA will tell us the main effect and interaction effect. The main effect is where music and age affect performance is measured like one way ANOVA. The interaction effect is where both age and the effect of music is measured at the same time.

Multivariate ANOVA

Multivariate ANOVA is when we study the impact of other factors for example if the use of music improves the score of children studying math’s but adversely impacts the students studying history. Therefore, now two groups i.e. history and math’s students will be tested with no music and constant music. Therefore, we have one-factor music with two levels and how the factor will impact our two dependent variables i.e. test scores of both math and history.

Some experts believe that it should be called an analysis of mean or ANOME instead of ANOVA because it compares the mean value of the variables. It is ANOVA because it also compares the variances. Suppose we have three different groups so there will be variation within the group and amongst the group too. ANOVA compares both variances within and amongst the groups. The two variances are between and within. Between i.e sum of the differences of the mean. Within i.e. the residual sum of squares. Only after applying the mean square you can apply F statistic. The mean squares can be calculated only after calculating the variances “between” and “within”. Hence it is called ANOVA