Statistical Analysis

1
Topic 9

• Statistical Analysis
• 1

2
Measurement Scales

• Nominal scales
• Gender, grade
• Ordinal scales
• Rank
• Interval scales
• Temperature scale
• Attitudinal data
• Ratio scales
• Weight, height, money amounts

3
Measurement Scales

• Non-metric scales
• Nominal scales
• Ordinal scales
• Metric scales
• Interval scales
• Ratio scales

4
Chi-Square Test

• Definition
• Test of the goodness of fit between the observed
  distribution and the expected distribution of a
  variable
• Components
• Chi-Square goodness of fit test
• Deal with one non-metric question
• Chi-Square for cross tabulation
• Deal with two non-metric questions
• Always one-tail test

5
Formula for Chi-Square goodness of fit Test

• where
• Oi observed number in ith category
• Ei expected number in ith category
• k number of categories

6
Steps In Hypothesis Testing

• State the Null and Alternative hypothesis
• Identify the appropriate test statistic
• Determine whether the test is one-tailed or
  two-tailed
• Obtain the critical value(s) of the test
  statistic
• Specify the decision rule
• Compute the value of the test statistic
• Reject or do-not-reject the null hypothesis

7
Example 1 (Chi-Square goodness of fit test)

• The population of interest is the UCF
  undergraduate students, suppose freshmen account
  for 15 of the total population, sophomores 35,
  juniors 25, and senior 25.
• You conducted a survey, which the sample size is
  280. And in your sample, there are 60 freshmen,
  80 sophomores, 55 juniors and 85 seniors. Conduct
  a statistical test to determine whether the
  sample matches the population.

8
Example 2 (Chi-Square goodness of fit test)
Conduct a statistical test to determine whether
shoppers have preferences among these three
stores.
9
Example 3 (Chi-Square goodness of fit test)

• A store managers computer-generated list of all
  retail sales employees indicates that 70 percent
  are full-time employees, 20 percent are part-time
  employees, and 10 percent are furloughed or
  laid-off employees.
• A sample of 50 employees from the list indicates
  that there are 40 full-time employees, 6
  part-time employees, and 4 furlough/laid-off
  employees. Conduct a statistical test to
  determine whether the sample is representative of
  the population.

10
Chi-Square for Cross Tabulation

• Deal with two non-metric questions
• To determine whether there is any association
  between two variables
• Always one-tail test

11
Formula for Chi-Square for Cross Tabulation

• where
• Oij observed number in ith row of the jth
  column
• Eij expected number in ith row of the jth
  column
• r number of rows
• k number of columns

12
Example 1 (Chi-Square for Cross Tabulation)

• A convenience store chain wants to determine the
  nature of the relationship between gender of
  customer and the frequency of visiting stores in
  the chain. The frequency distribution of the
  sample size 116 is as follows

13
Example 2 (Chi-Square for Cross Tabulation)
Conduct a statistical test to determine whether
there is relationship between gender and time of
playing the toys.
14
Example 3 (Chi-Square for Cross Tabulation)

• Determine whether there is association between
  the age of the shopper and their preference of
  the store.