PACKAGE: BSDA

GENERAL FORM OF R COMMAND:

z.test(dataframename$variablename, alternative = " ", mu = munull, sigma.x = knownstandarddeviation, conf.level = 0.95)

alternative could be equal to "greater", "less", or "two.sided".

EXAMPLE:

Dataset:

We are asked to analyze the average height of individuals of Italian nationality. The variance of the Italian population is known to be 5. Here is the data:

175, 168, 168, 190, 156, 181, 182, 175, 174, 179

We will test the hypothesis that the true mean height is different than 170, and construct a confidence interval.

Since the data set is small we will enter the data directly to R without using a data frame.

a = c(175, 168, 168, 190, 156, 181, 182, 175, 174, 179)

library(BSDA)

z.test(a, alternative = "two.sided", mu = 170, sigma.x = 2.24, conf.level = 0.95)

Note that we have been given the varaince, you need to take the square root of 5 for the standard deviation.

EXERCISE: Construct a 99% confidence interval for this problem

GENERAL FORM OF R COMMAND:

t.test(dataframename$variablename, alternative = " ", mu = munull, conf.level = 0.95)

alternative could be equal to "greater", "less", or "two.sided".

EXAMPLE:

Dataset:

We are asked to analyze the average height of individuals of Italian nationality. Here is the data:

175, 168, 168, 190, 156, 181, 182, 175, 174, 179

We will test the hypothesis that the true mean height is different than 170, and construct a confidence interval.

Since the data set is small we will enter the data directly to R without using a data frame.

a = c(175, 168, 168, 190, 156, 181, 182, 175, 174, 179)

t.test(a, alternative = "two.sided", mu = 170, conf.level = 0.95)

EXERCISE: Test the hypothesis that mean height is more than 170.

GENERAL FORM OF R COMMAND:

t.test(dataframename$variablename1, dataframename$variablename1, paired = TRUE, alternative = " ", mu = munull, conf.level = 0.95)

alternative could be equal to "greater", "less", or "two.sided".

EXAMPLE:

Dataset:

In this example we will compare affect of a new training on 100 meter runners. The following data gives time in seconds before and after training for 10 randomly selected athletes.

Before: 12.9, 13.5, 12.8, 15.6, 17.2, 19.2, 12.6, 15.3, 14.4, 11.3

After: 12.7, 13.6, 12.0, 15.2, 16.8, 20.0, 12.0, 15.9, 16.0, 11.1

We will test the hypothesis that the true mean performances for these groups are different and construct a confidence interval for the difference between mean performances.

Since the data set is small we will enter the data directly to R without using a data frame.

Before = c(12.9, 13.5, 12.8, 15.6, 17.2, 19.2, 12.6, 15.3, 14.4, 11.3)

After = c(12.7, 13.6, 12.0, 15.2, 16.8, 20.0, 12.0, 15.9, 16.0, 11.1)

t.test(Before, After, paired = TRUE, alternative = "two.sided", mu = 0, var.equal = FALSE, conf.level = 0.95)

EXERCISE: Construct a 90% confidence interval for the difference between means.

DATA FORMAT: Two columns; response variable (numerical) and treatments (factors) as follows

Response	Treatment

GENERAL FORM OF R COMMAND:

aov(response ~ treatment, data = dataframename)

EXAMPLE:

Dataset: donut.csv

Twenty four batches of donuts were prepared and six radomly assigned to each of the four fats. The amount of fat absorbed for each batch (in grams) were measured. Upload and load the data into RStudio. Here is the data

Fat1	Fat2	Fat3	Fat4
164	178	175	155
172	191	193	166
168	197	178	149
177	182	171	164
156	185	163	170
195	177	176	168

Note that the data is not in the format to be used in R so we will stack the data.

donut <- read.csv(file.choose())

sdonut = stack(donut)

This will create a data frame with variable names values and ind.

sdonut

summary(donut)

attach(sdonut)

boxplot(values ~ ind)

aov(values ~ ind, data = sdonut)

To see the ANOVA table

donut.aov = aov(values ~ ind, data = sdonut)

summary(donut.aov)

 

DATA FILE: Data file should look like the following.

	Column Level 1	...	Column Level c
Row Level 1	count		count
...
Row Level r	count		count

GENERAL FORM OF R COMMAND:

chisq.test(data.matrix, correct = FALSE)

EXAMPLE:

Dataset: Handedness.csv

The table gives you offspring being left-handed and parental handedness. For the parental handedness fir one is for father the second one is for mother. Click on the file to download it and move it into RStudio.

STEP 1. Create a data file outside of R by using Excel just like given above. Note that you give a variable name for the row categorical variable. In this example it is "Father.Mother". Download and load the file to RStudio. In this case this has been already done.

Handedness <- read.csv(file.choose(), row.names = "Father.Mother")

STEP 2. Carry out the chi-square test

testresult <- chisq.test(Handedness, correct = FALSE)

testresult

STEP 3. If significant get observed andexpected counts, residuals and standardized residuals.

testresult$observed
testresult$expected
testresult$residuals
testresult$stdres

STEP 4. Produce a graphical display.

barplot(t(prop.table(Handedness)), beside = TRUE, xlab = "Parental Handedness", ylab = "Proportion", legend = T)

mosaicplot(Handedness, shade = TRUE, main = "Genetics and Handedness")

NOTE:

Cell percentages:
prop.table(data.matrix)

Row percentages:
prop.table(t(data.matrix), 1)

Column percentages:
prop.table(t(data.matrix), 2)

EXERCISE: The data were obtained by asking large number of people in the UK which of 13 characteristics they would associate with the nationals of the UK's partners in the European Community.

Load the following data and analyze it. In this case row variables name is "Country".

UKPerceptionsofEuropeans.csv

 

GENERAL FORM OF R COMMAND:

chisq.test(data.matrix, correct = FALSE)

EXAMPLE:

Randomly selected subjects by the Pew Research Center were asked about the use of marijuana for medical purposes and their genders have been noted. Here is the frequency table:

	Infavor	Oppose	Don't Know
Men	538	167	29
Women	557	186	31

STEP 1. Create a data matrix. We will create the matrix from the rows and name the columns.

Men = c(538, 167, 29)

Women = c(557, 186, 31)

data.table = rbind(Men, Women)

colnames(data.table) = c("In favor", "Oppose", "Don't Know")

STEP 2. Carry out the chi-square test

testresult <- chisq.test(data.table, correct = FALSE)

testresult

STEP 3. If significant get observed andexpected counts, residuals and standardized residuals.

testresult$observed
testresult$expected
testresult$residuals
testresult$stdres

STEP 4. Produce a graphical display.

barplot(t(prop.table(data.table)), beside = TRUE, xlab = "Gender", ylab = "Proportion", legend = T)

mosaicplot(data.table , shade = TRUE, main = "The Use of Marijuana")

EXERCISE: The following tables are from a study on Eye-Dominance, Writing Hand, and Throwing Hand relationships. To see the original paper click here. If you would like to determine your dominant eye visit this site.

Analyze the tables by using the technique that you have learned in this section.

Eye- Dominance	Writing Hand
	Right	Left
Right	544	56
Left	251	83

Throwing Hand	Writing Hand
	Right	Left
Right	544	56
Left	251	83

Eye-Dominance	Throwing Hand
	Right	Left
Right	544	56
Left	251	83