Stat 350 Lab Session GSI: Yizao Wang Section 016 Mon 2pm30-4pm MH 444-D Section 043 Wed 2pm30-4pm MH 444-B

Outline Introduction Syllabus A brief review Module1: Activity1,2 Module2: Activity2

Something about me My name: Yizao Wang My brief CV: Originally from Beijing Having been studying in Paris during the last three years Now a first year graduate student in Department of Statistics I play Go when I have time… (do you know where is the Umich Go club?)

Introduce yourself What is your name? Where are you from? What is your major? Which year are you in?

Syllabus Any questions?

What is statistics… Data | Analysis | Inference/conclusion

Let’s start with data When we are collecting (sampling) data…  How many types of variables are there?  What are they?

Let’s start with data When we are collecting (sampling) data…  How many types of variables are there? 2  What are they? Categorical variables Quantitative/numerical variables

CategoricalQuantitative Raw data Consisting of groups of names that do not necessarily have a logical order Consisting of numerical values taken on each individual. exampleGender, eye colorHeight, test score Graphical summary Numerical summary

CategoricalQuantitative Raw data Consisting of groups of names that do not necessarily have a logical order Consisting of numerical values taken on each individual. exampleGender, eye colorHeight, test score Graphical summary Bar graph Pie chart Histogram Boxplot Numerical summary

CategoricalQuantitative Raw data Consisting of groups of names that do not necessarily have a logical order Consisting of numerical values taken on each individual. exampleGender, eye colorHeight, test score Graphical summary Bar graph Pie chart Histogram Boxplot Numerical summary Frequency table 5 number summary (median, quartiles and extremes)

Some big ideas  Different types of data lead to different statistical methods, numerical summaries and plots.  Histograms: the (shape of ) distribution of a quantitative response  Boxplots: picture of 5 number summary most useful for comparing 2+ sets of data

Module 1: Activity 1 visualizing and exploring a data set  Start up SPSS and open the employee data set  What type of variable is gender?  What type of graphs would be good to make for this variable?  What type is current salary?  What type of graphs for it?

Module 1: Activity 1 visualizing and exploring a data set  Start up SPSS and open the employee data set  What type of variable is gender? Categorical  What type of graphs would be good to make for this variable? Bar graphs  What type is current salary? Quantitative  What type of graphs for it? Histogram

Module 1: Activity 1 visualizing and exploring a data set  Let’s make a histogram of current salary  Don’t forget the title!  What shape do we see for the distribution of salary?  Change the color

Module 1: Activity 1 visualizing and exploring a data set  Let’s make a histogram of current salary  Don’t forget the title!  What shape do we see for the distribution of salary? Skew to the right  Change the color

Module 1: Activity 1 visualizing and exploring a data set  Basic summary measures for current salary  Get five number summary  Save output

Module1: Activity 2 The Mean and the Median  Open the applet m/descriptive/index.html m/descriptive/index.html  Produce a positive skew and a negative skew, and compare the relationship between the mean and the median  Try different shapes of distribution, compare their standard deviations. Comment? Toy question: with N=10, give the distribution with largest/smallest standard deviation

Module1: Activity 2 The Mean and the Median  In a symmetric distribution, the mean and the median are equal.  With positive skewed distributions, the mean is generally larger than the median.  With negative skewed distributions, the mean is generally smaller than the median.  In a skewed distribution, which is a good measure the center of a distribution?

Module1: Activity 2 The Mean and the Median  In a symmetric distribution, the mean and the median are equal.  With positive skewed distributions, the mean is generally larger than the median.  With negative skewed distributions, the mean is generally smaller than the median.  In a skewed distribution, which is a good measure the center of a distribution? Median

Module1: Activity 2 The Mean and the Median  Standard deviation: On average, salaries are expected to fall approximately ___$ from the mean salary of ___$. On average, salaries vary by about ___$ from the mean salary of ___$.

Module2: Activity 1 How do genders compare on SSHA scores  Background: Survey of Study Habits and Attitudes of college freshmen. It is known that scores on the SSHA may explain success in college. Data of both females and males is collected.  Use side-by-side boxplots to examine (compare) the distribution of the scores by gender.

Module2: Activity 1 How do genders compare on SSHA scores  Produce a side-by-side boxplot Add a title  Which gender had the lowest score?  Which had the highest score?  Which gender had the lowest median score?  How to compare the variability?  Can you tell the shape from boxplot?

Module2: Activity 1 How do genders compare on SSHA scores  Produce a side-by-side boxplot Add a title  Which gender had the lowest score? Male  Which had the highest score? Female  Which gender had the lowest median score? Male  How to compare the variability? IQRs  Can you tell the shape from boxplot? No!

Module2: Activity 1 How do genders compare on SSHA scores  Split file and make histograms (organize output by groups)  (Get descriptive summaries using frequencies option)

Review of lab 1  What does statistics do?  Categorical variables and numerical variables  Using plots to visualize data  Histogram to see the distribution  Standard deviation and shape of distribution  Boxplot with 5 number summary  Are you able to do HW1 with SPSS?

Before we finish today…  Comments on today’s lab?  Qwizdom system  Survey to complete