Question

1.

A researcher decides to compare three groups of subjects on a decision-making task, to see if people make riskier decisions when their friends were around. She compares three groups, either with their friends present, absent, or a stranger nearby. She conducts a one-way between-subjects ANOVA and obtains the following values for her F-table

Source of Error	SS	df	MS	F
BG	2024	2	1012	3.42
Error	5328	18	296
Total	14712	20

2.

A researcher is interested in studying if different methods for commuting lead to greater happiness. He tests three groups: drivers, train riders, and bike riders. Each group completes a happiness questionnaire, with higher values indicating greater happiness. She collects the following data.

Drivers	Train Riders	Bike Riders
5	17	92
7	17	24
13	33	52
41	55	60
28	47	60
59	74	94
37	57	72

Calculate the test statistic (F-obtained) for this statistical test (One-way Between Subjects ANOVA)

Answer 1

1. A researcher decides to compare three groups of subjects on a decision-making task, to see if people make riskier decisions when their friends were around. She compares three groups, either with their friends present, absent, or a stranger nearby. She conducts a one-way between-subjects ANOVA and obtains the following values for her F-table

Here we have to test the hypothesis that,

H0 : people do not make riskier decisions when their friends were around.

H1 : people make riskier decisions when their friends were around.

Assume alpha = level of significance = 0.05

Test statistic F = 3.42

Now we have to find P-value for taking decision.

We can find P-value in excel.

syntax :

=FDIST(x, deg_freedom1, deg_freedom2)

where x is test statistic

deg_freedom1 = 2

deg_freedom2 = 18

P-value = 0.0551

P-value > alpha

Accept H0 at 5% level of significance.

Conclusion : People do not make riskier decisions when their friends were around.

Three groups population means are same.

2. A researcher is interested in studying if different methods for commuting lead to greater happiness. He tests three groups: drivers, train riders, and bike riders. Each group completes a happiness questionnaire, with higher values indicating greater happiness. She collects the following data.

This is also one way anova.

We can do one way anova in excel.

syntax :

ENTER data into excel sheet --> Data --> Data analysis --> Anova : single factor --> Ok --> Input range : select all the data together --> Labels in first row --> Alpha : 0.05 --> Output range : select one empty cell--> ok

Test statistic F= 5.20