Rapport package team
 Bartlett's test
 2011-04-26 20:25 CET

Contents
•	Description
–	Introduction
–	Normality assumption
–	Test results
•	Description
–	Introduction
–	Normality assumption
–	Test results
•	Description
–	Introduction
–	Normality assumption
–	Test results
Description
This template will run the Bartlett's test to check the equality of variances between groups.
Introduction
Bartlett's test is used to test the homogeneity of the variances, in other words the equality of the tested variable's variances across the groups. With checking that we want to find if the two groups are coming from the same population.
Homogeneity is useful to being tested, because that is an assumption of the One-Way ANOVA.
References
•	Snedecor, George W. and Cochran, William G. (1989). Statistical Methods. Iowa State University Press
Normality assumption
The Bartlett's test has an assumption of normality, thus one should obtain the information if the distribution of the tested variable had a normal distribution.
We will use Shapiro-Wilk, Lilliefors and Anderson-Darling tests to screen departures from normality in the response variable.
Method
	Statistic
	p-value
	
Lilliefors (Kolmogorov-Smirnov) normality test
	0.17
	6.193e-54
	
Anderson-Darling normality test
	32.16
	1.26e-71
	
Shapiro-Wilk normality test
	0.8216
	9.445e-27

So, the conclusions we can draw with the help of test statistics:
•	based on Lilliefors test, distribution of Age is not normal
•	Anderson-Darling test confirms violation of normality assumption
•	according to Shapiro-Wilk test, the distribution of Age is not normal
As you can see, the applied tests confirm departures from normality.
Test results
After checking the assumptions let's see what the test shows us!
Method
	Statistic
	p-value
	
Bartlett test of homogeneity of variances
	0.233
	0.6293

According to the Bartlett's test, the variance of the Age across the groups of Gender does not differs significantly.
We can conclude that, because the p-value is higher than 0.05.
Description
This template will run the Bartlett's test to check the equality of variances between groups.
Introduction
Bartlett's test is used to test the homogeneity of the variances, in other words the equality of the tested variable's variances across the groups. With checking that we want to find if the two groups are coming from the same population.
Homogeneity is useful to being tested, because that is an assumption of the One-Way ANOVA.
References
•	Snedecor, George W. and Cochran, William G. (1989). Statistical Methods. Iowa State University Press
Normality assumption
The Bartlett's test has an assumption of normality, thus one should obtain the information if the distribution of the tested variable had a normal distribution.
We will use Shapiro-Wilk, Lilliefors and Anderson-Darling tests to screen departures from normality in the response variable.
Method
	Statistic
	p-value
	
Lilliefors (Kolmogorov-Smirnov) normality test
	0.2223
	2.243e-92
	
Anderson-Darling normality test
	42.04
	3.31e-90
	
Shapiro-Wilk normality test
	0.7985
	6.366e-28

So, the conclusions we can draw with the help of test statistics:
•	based on Lilliefors test, distribution of Internet usage for educational purposes (hours per day) is not normal
•	Anderson-Darling test confirms violation of normality assumption
•	according to Shapiro-Wilk test, the distribution of Internet usage for educational purposes (hours per day) is not normal
As you can see, the applied tests confirm departures from normality.
Test results
After checking the assumptions let's see what the test shows us!
Method
	Statistic
	p-value
	
Bartlett test of homogeneity of variances
	36.11
	1.863e-09

According to the Bartlett's test, the variance of the Internet usage for educational purposes (hours per day) across the groups of Student significantly differs.
We can conclude that, because the p-value is smaller than 0.05.
Description
This template will run the Bartlett's test to check the equality of variances between groups.
Introduction
Bartlett's test is used to test the homogeneity of the variances, in other words the equality of the tested variable's variances across the groups. With checking that we want to find if the two groups are coming from the same population.
Homogeneity is useful to being tested, because that is an assumption of the One-Way ANOVA.
References
•	Snedecor, George W. and Cochran, William G. (1989). Statistical Methods. Iowa State University Press
Normality assumption
The Bartlett's test has an assumption of normality, thus one should obtain the information if the distribution of the tested variable had a normal distribution.
We will use Shapiro-Wilk, Lilliefors and Anderson-Darling tests to screen departures from normality in the response variable.
Method
	Statistic
	p-value
	
Lilliefors (Kolmogorov-Smirnov) normality test
	0.17
	6.193e-54
	
Anderson-Darling normality test
	32.16
	1.26e-71
	
Shapiro-Wilk normality test
	0.8216
	9.445e-27

So, the conclusions we can draw with the help of test statistics:
•	based on Lilliefors test, distribution of Age is not normal
•	Anderson-Darling test confirms violation of normality assumption
•	according to Shapiro-Wilk test, the distribution of Age is not normal
As you can see, the applied tests confirm departures from normality.
Test results
After checking the assumptions let's see what the test shows us!
Method
	Statistic
	p-value
	
Bartlett test of homogeneity of variances
	23.26
	0.0001123

According to the Bartlett's test, the variance of the Age across the groups of How often does your profession require Internet access? significantly differs.
We can conclude that, because the p-value is smaller than 0.05.
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