LSP 121. LSP 121 Math and Tech Literacy II. Topics. Quartiles. Intro to Statistics. More Descriptive Statistics

Transcription

1 Greg Brewster, DePaul University Page 1 LSP 121 Math and Tech Literacy II More Descriptive Statistics Greg Brewster DePaul University Topics More Descriptive Statistics Quartiles Percentiles Categorical vs. Numeric Variables Crosstabs SPSS Predictive Analysis Software (PASW) Basic Descriptive Stats Graphs Histograms Crosstabs Quartiles Lower quartile or first quartile, is the median of the data values in the lower half of a data set. One-quarter of the data set values are less than the first quartile value. Middle quartile or second quartile, is the median value. Half the dataset values are less than the middle quartile value Upper quartile or third quartile, is the median of the data values in the upper half of a data set. Three-quarters of the values are less than the upper quartile. 3

2 Greg Brewster, DePaul University Page 2 Calculating Quartiles Middle quartile = the dataset median (see last class notes on calculating median) Lower quartile = the median of all values less than the dataset median (do not include the median) Upper quartile = the median of all values greater than the dataset median (do not include the median) 4 Quartiles For example (bank waiting times): lower quartile median upper quartile Big Bank: Best Bank: Big Bank range: = 6.9 Best Bank range: = Definition: the Y percentile value, P Y in a data set is the value, X, for which Y% of all values in the data set are less than or equal to X. Percentiles Examples: 20% of the values in a data set are less than or equal to the 20 th percentile value. The 50 percentile value P 50 is the median. 6

3 Greg Brewster, DePaul University Page 3 Quartiles and Percentiles Quartiles are specific percentiles Lower quartile = 25 th percentile Middle quartile = 50 th percentile Upper quartile = 75 th percentile 7 Example: an ordered data set is: 39, 40, 47, 58, 60 Percentiles What is the 80 th percentile - or P 80? Answer: since the data set has 5 values and 80% of 5 = 4 (5x(80/100) = 4), the 80 th percentile, P 80 is the fourth value (position 4), which is % of the values in the data set (39, 40, 47, 58) are less than or equal to The Five Number Summary The five number summary of a data set consists of: The minimum value The lower quartile (first quartile) The median (second quartile) The upper quartile (third quartile) The maximum value 9

4 SPSS PASW We will use Predictive Analytics SoftWare (PASW) version 17.0 from SPSS, Inc to do our statistical analysis. PASW Data sets can hold various types of data 10 PASW has the same data types as we saw in Microsoft Access: String (the PASW name for Text) Numeric - User indicates #digits needed before and after the decimal point, and PASW chooses storage size. Date Currency PASW Data Types 11 Categorical Data In statistics, text data is often called categorical data, because it represents measurements of categories. Examples: categorical titles and values: Gender: Male, Female Eye color: Blue, Grey, Green, Brown Satisfaction Level: Very Dissatisfied, Dissatisfied, Neutral, Satisfied, Very Satisfied Grade: A, A-, B+, B, B-, C+, C, C-, D+, D, F 12 Greg Brewster, DePaul University Page 4

5 Types of Categorical Data PASW utilizes two different types of categorical data: Nominal: data values have no particular ordering. Examples: Gender, Eye Color Ordinal: data values have an ordering Examples: Satisfaction levels, Grades 13 Categorical Data Statistics Only some descriptive statistics make sense for categorical data: Nominal data: Useful: Frequency, Mode Not Meaningful: Mean, Median, Percentiles, Range, Standard Deviation Ordinal data: Useful: Frequency, Mode, Median, Percentiles, Range Not Meaningful: Mean, Standard Deviation (unless you associate a number with each value) 14 Frequency Table Remember, last time we look at Frequency Tables. For example: Height Frequency Greg Brewster, DePaul University Page 5

6 Greg Brewster, DePaul University Page 6 Crosstabulations (Crosstabs) What if you want to look at frequency counts for 2 variables at the same time? Crosstabs show joint frequencies of two different variables. They are arranged in table format with a frequency listed for every possible pair of variable values. 16 Example Let s say that we asked 10 high school seniors how many colleges they have applied to 17 Data ID Gender Schools 1 F 2 2 M 6 3 F 1 4 F 4 5 M 4 6 M 1 7 F 3 8 F 2 9 F 5 10 M 5 18

7 Greg Brewster, DePaul University Page 7 Frequency Table Frequency table for Schools data (both genders) # Schools Frequency CrossTab Crosstabulation for Schools over Gender Totals M F Totals Common PASW Commands Draw a graph Graphs -> Chart Builder Descriptive Statistics Analyze -> Descriptive Statistics Set Binning Transforms -> Visual Binning 21