Statistical Estimation

UNG MATH 3350 (online)

I. Initialization Block

Initializing RStudio

The data set we will use primarily is Data3350 which was produced in 2015 during an undergraduate research project about personality and humor. The VarsData3350 PDF file has descriptions of each variable in the Data3350 file. Both are available for download in D2L. Be sure to put the Data3350 in your R folder in Documents, and make sure your working directory is set the same way (Session menu). The code block below uses the library function to ensure that the Mosaic package is loaded and will import the data frame used in this module: Data3350.

library(mosaic)
library(readxl)
Data3350 = read_excel("Data3350.xlsx")

II. Exercises

1. How many resamplings should we use when bootstrapping? Try re-running the code blocks from the Sleep example with 50, 100, 500, and 1000 resamplings. How does the accuracy compare to the theoretical confidence interval as number of resamplings increases? Explain why about 500 resamplings is usually good enough.

Code Block: Question 1

bootstrap = do(50) * mean(resample(Data3350$Sleep))
qdata(~mean, p=c(0.025, 0.975), data=bootstrap)

2. Use the Corps variable in Data3350 where Y / N responses indicate whether the participant’s is in the UNG Corps of Cadets. Assuming the data frame is representative of the UNG Dahlonega campus, create a 90% confidence interval estimate for the percentage of students who are members of the Corps and interpret your findings. Hint: set success = “Y”.

3. Use the VarsAth variable in Data3350 where Y / N responses indicate whether the participant’s is a varsity UNG athlete. Assuming the data frame is representative of the UNG Dahlonega campus, create a 95% confidence interval estimate for the percentage of students who are varsity athletes and interpret your findings. Hint: set success = “Y”.

Mosaic’s Randomization Options

1. Shuffle. Permutes the values in the sample data.
2. Sample. Draws a sub-sample from the sample data
   without replacement.
3. Resample. Draws a sub-sample from the sample data
   with replacement.
   

For examples of permutation tests and bootstrapping, see
the Randomization Tutorial.

4. Use the TexRel variable in Data3350 where numeric scores represent scores on the Toxic Relationship Beliefs Scale. (Higher scores equate to more toxic beliefs). Assuming the data frame is representative of the UNG Dahlonega campus, create a 99% confidence interval estimate for the mean TxRel score and interpret your findings.

5. Use the CHS variable in Data3350 where numeric scores represent scores on the Coping Humor Scale. Assuming the data frame is representative of the UNG Dahlonega campus, create a 95% confidence interval estimate for the mean CHS score and interpret your findings.

6. Use the CHS variable in Data3350 to create a bootstrap confidence interval at the 95% level. Compare and contrast it with the results from the theoretical confidence interval. Use 500 resamplings.

III. Code Blocks

library(mosaic)
library(readxl)
Data3350 = read_excel("Data3350.xlsx")

cdist("norm", 0.95)

cdist("norm", 0.95 , plot = FALSE)*15+100

cdist("norm", 0.95, plot = FALSE)*3 +111

qdata(rnorm(500), p=c(0.025, 0.975))

qdata(rnorm(500)*3+111, p=c(0.025, 0.975))

cdist("t", df = 24, 0.95)

cdist("t", 0.95, df = 24, plot = FALSE)*1.8 + 111

histogram(~Sleep, data = Data3350)

favstats(~Sleep, data = Data3350)

confint(t.test(~ Sleep, data = Data3350))

mean(temp)

bootstrap = do(500) * mean(resample(Data3350$Sleep))
bootstrap

densityplot(~mean, data=bootstrap)

qdata(~mean, p=c(0.025, 0.975), data=bootstrap)

tally(~SitClass, data = Data3350)

confint(prop.test(~SitClass, success = "F", data = Data3350))

seat = resample(Data3350$SitClass)
seat
prop(seat , success = "F")

boots = do(500) * prop(resample(Data3350$SitClass),success = "F")
histogram(~prop_F, data = boots)

qdata(~prop_F, p=c(0.025, 0.975), data=boots)

fem = subset(Data3350, Sex == "F", c(Age,HSAG))
yF = subset(fem, Age < 20, HSAG)
yFem = na.omit(yF)
yFem

bootstrap = do(500) * mean (resample(yFem$HSAG))
bootstrap

qdata(~mean, p=c(0.05, 0.95), data=bootstrap)