Statistics

1
Statistics YouPerfect Together

• There are three kinds of lies lies, damned lies,
  and statistics.
• Benjamin Disraeli

2
Data Types

• nominal things that cannot be ordered
• position on basketball team, state born in
• ordinal categories that can be ordered, or
  quantitative data that doesnt fit into the other
  data types
• Likert scale data

3
Data Types

• interval-ratio categories are ordered and
  measurements are in the same unit, i.e, the
  difference between them has a clear
  interpretation
• age, salaries, test scores, temperature

4
Measures of Central Tendency

• Mean ( ) arithmetic average
• sum of data divided by amount of data
• Excel AVG(range)
• Median middle number
• 50 above median, 50 below median
• Excel MEDIAN(range)
• Mode most common number
• Excel MODE(range)

5
Measures of Dispersion

• Standard Deviation measures the spread
• small s means data values are close
• large s means data values are far
• Excel STDEV(range)
• Range difference between largest and smallest
  value
• Excel (MAX(range) MIN(range))

6
Measures of Dispersion

• Normal Distribution, aka Bell Curve
• mean median mode
• 68 of data within 1s of mean (34 each side)
• 95 of data within 2s of mean (47.5 each side)
• 99 of data within 3s of mean (49.5 each side)

7
Graphical Displays of Data

• Bar Graph
• shows differences in frequencies or percentages
  of a nominal or ordinal variable
• Excel Use Chart Wizard

8
Graphical Displays of Data

• Histogram
• shows differences in frequencies or percentages
  of an interval-ratio variable

9
Graphical Displays of Data

• Circle Graph
• shows differences in frequencies or percentages
  of a nominal or ordinal variable
• Excel Use Chart Wizard

10
Graphical Displays of Data

• Box ( Whisker) Plot
• range, quartiles, interquartile range, maximum,
  minimum, median
• http//www.coventry.ac.uk/ec/nhunt/boxplot.htm

11
Some Excel Practice

• ONE-VAR STATS worksheet
• Calculate mean, median, mode, standard deviation,
  range
• GRAPH DATA worksheet
• Create a Circle Graph Bar Graph for each set of
  data

12
Comparison of Two Variables

• Correlation coefficient
• test of a linear relationship between two
  variables
• T-Test
• used to test whether two samples are likely to
  have come from the same two underlying
  populations that have the same mean
• Chi Square Test (c2)
• test of a significant relationship between two
  variables

13
Correlation

• called the correlation coefficient (r)
• Excel CORREL(range)
• CORRELATION DOES NOT IMPLY CAUSATION!

14
Example for Correlation

• if r is near 1, there is a positive relationship
• if r is near 0, there is no relationship
• if r is near -1, there is a negative relationship

15
Example for Correlation

• AIDS/HIV deaths in NYC from 1986-1994
• Excel Worksheet CORREL

16
Example for the T-test

• Sample of 150 white women (in 1998) who work full
  time mean income 26,078 and s 21,751
• We know that mean income of all working women (in
  1998) is 20,410
• Research Hyp mean ? 26,078
• Null Hyp mean 26,078

17
Example for the T-test

• calculation results in a t value of 3.19
• we can interpret this (with the help of a table)
  to correspond to the 0.01 level of significance
• This means that we reject the null hyp the mean
  income for white women IS NOT the same as mean
  income for all women

18
Example for the Chi Square Test

• Note that data is with actual numbers!
• No percents, proportions, means, etc

19
Example for the Chi Square Test

• Calculations of expected results assumes same
  proportions/percentages for men women

20
Example for the Chi Square Test

• we can conclude that the probability that this
  difference would occur randomly is less than .001