# Perform a Two Population Hypothesis Test

Give a work example and perform a hypothetical 2 population hypothesis test.

Discuss an application of ANOVA that might be undertaken in your workplace. What are the 3 or more treatments? What is the response variable?

Create a scenario and do a hypothesis testing example for ANOVA. Give the result and explain what it means.

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

ANOVA stands for Analysis of Variance. ANOVA is a statistical technique that examines the differences between three or more groups of participants or conditions and determines whether the amount of variance between the groups is greater than the variance within the groups. The way we do it is to compare the means of the different groups. So we test a hypothesis about several means.

H0: Âµ1 = Âµ2 = Âµ3 = Âµ4

In ANOVA there is at least one independent variable, which consists of different categories and a numerical dependent variable. I will explain them with an example (remember you have to use your own example from your work). I will give you an example for academics. Say there are two groups of students (graduate and undergraduate) and they are taught by two different teaching methods (method 1 and method 2). So, a researcher might be interested to find out how well undergraduate and graduate students will learn when taught by two different teaching methods. In this case student's learning ability is the dependent or response variable. Also the two groups of students and two teaching methods are the independent variables.

The design for this particular type of ANOVA is known as two-factor independent-group design. A simple observation of the data tells us that the test score for a graduate or undergraduate student depends on either method 1 or method 2. In other words we need to consider both factors together to understand a test score. Therefore, we can define four groups: "undergraduate, method 1", "undergraduate, method 2", "graduate, method 1", "undergraduate, method 2". These groups are known as treatments. In other words, treatment is a particular combination of a level of one factor and a level of another factor.

When you perform an ANOVA test with a statistical software, it will always give you a summary table.

Following are the components ANOVA summary table:

i) Group Totals, and Grand Total

ii) Group Means and Grand Mean

iii) Correction Factor (CF): square of the grand total divided by the total number of scores: CF=(∑X)2/n

iv) Total Sum of Squares: Total SS =∑X2-CF

v) Between-Groups Sum of Squares: Between-Groups SS =(Group Totals) 2/n - CF

vi) Within-Groups Sum of Squares: Total SS - Between-Groups SS or 12

vii) Degrees of Freedom (df)

a) Total df = Total number of scores - 1

b) Between-Groups df = Total number of groups - 1

c) Within-Groups df = Total df - Between-Groups df

viii) Mean Squares (MS)

a) Between-Group MS = (Between-Groups SS)/(Between-Groups df)

b) Within-Groups MS = (Within-Groups SS)/(Within-Groups df)

ix) The F ratio: The between-groups MS/the within-groups MS

x) The P level (p < 0.05 Level of significance means that the probability of getting the result by chance alone is less than 5%).

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