8/29/2016

Discussion of Sampling Activity

• Put sticky notes on the white boards for all three statistics we decided to compare near the end of our first class session
• Which statistic is best? Why?

Types of Variables

• A quantitative variable is a variable that takes on numerical values for which arithmetic makes sense.
• A categorical or qualitative variable is a variable that records which category a person place or thing falls into.

Questions about data

• What variables are being measured?
• Are these variables appropriate for answering the question(s) of interest?
• What are the units of measurement?
• How are the data recorded?

Graphical Displays

• Why are graphing techniques useful?
  • Examine the overall shape of a distribution - (symmetric or skewed?)
  • Look for deviations from the overall shape - (unusual observations, gaps, etc.)
  • Locate the center of the distribution

Stem and Leaf Plots

• Separate each observation into a stem and a leaf.
• List the stems vertically in increasing order from top to bottom.
• Add the leaves (typically the last digit) to the right of the stems.

Histograms

• Divide the range of the data into classes of equal width.
• Count the number of observations in each class.
• Compute the relative frequency or percent for each class.
• Erect bars over each class interval.

Getting started with R

• Lauch RStudio (you can download R and RStudio on your personal computer/laptop for free)
• Load our data from the class survey (P:\Data\MATH\STATS\Datasets\ClassDataF16.csv)
  • Method 1 - mydata=read.csv(file=file.choose())
  • Method 2 - ClassDataF16<-read.csv("P:/data/MATH/STATS/Datasets/ClassDataF16.csv")
• Some basic R
  • mydata
• str(mydata)
• head(mydata)
• tail(mydata)
• names(mydata)
• libarary(mosaic) -- a package that we will be using throughout the semester.

Graphical Displays with R (Use P:\data\math\stats\Datasets\ClassDataF16.csv)

• Bar Charts - bargraph(Year, data=mydata)
• Dotplots - dotplot(Height.in.Inches, data=mydata)
• Stemplots - stem(mydata$Height.in.Inches)
• Histograms - histogram(Height.in.Inches, data=mydata)
• Boxplots - boxplot(mydata$Haircut.cost), boxplot(mydata$Haircut.cost~mydata$Gender)
• Scatterplots - xyplot(y~x), plot(y~x)

In Class Exercises

1. Construct appropriate graphs to visually summarize the information collected on the class data survey for the following variables: Gender, Year, height, wingspan, age, hair cut cost, handedness, coins, whitestring, blackstring, TV, pulse, and text messages.
2. Is the shape of the distribution for guesses of the length of the black string the same as the distribution of guesses for the length of the white string?
3. The actual length of the white sting is 46". Is the overall distribution of guesses centered at this value?
4. The actual length of the black string is 48". Is the overall distribution of guesses centered at the appropriate value?
5. Use appropriate graphical displays and descriptive statistics to make appropriate comparisons between men and women for different variables in the data set we collected during the first class.
6. Use appropriate graphical displays and descriptive statistics to make appropriate comparisons between the four sections for different variables in the data set we collected during the first class.
7. (Do this exercise "by hand," not with R.) Caution is necessary when constructing histograms from frequency distributions given in magazines, newspapers, journal articles, etc.  The authors of "Self-Reports of Academic Performance," an article which appeared in Soc. Methods and Research (1981), studied the difference in GPA, reported - actual, for each of the students in a sample.  Specify the height of each bar in a correct histogram for the frequency distribution below and sketch the histogram.

  Frequency distribution for errors in reported GPA

Class Interval	Relative Frequency	Height
[-2.0, -0.4)	.023
[-0.4, -0.2)	.055
[-0.2, -0.1)	.097
[-0.1,  0.0)	.210
[ 0.0,  0.1)	.189
[ 0.1,  0.2)	.139
[ 0.2,  0.4)	.116
[ 0.4,  2.0)	.171

Please read Section 1.3 for class on Wednesday