Review: T test vs. ANOVA

1
Review T test vs. ANOVA

• When do you use T-test ?

• Compare two groups
• Test the null hypothesis that two populations has
  the same average.

• When do you use One-way ANOVA?

• Compare more than two groups
• Test the null hypothesis that two populations
  among several numbers of populations has the same
  average.

2
What kind of statistical test would you use for
the following situations? And why? Identify
independent variable(s) and a dependent variable.

• The Ware County librarian wants to increase
  circulation from the Ware County bookmobiles. The
  librarian thinks that poster ads in areas where
  the bookmobiles stop will attract more browsers
  and increase circulation. To test this idea, the
  librarian sets up an experiment. Ten bookmobile
  routes are selected at random on those routes,
  poster ads are posted with bookmobile
  information. Ten other bookmobile routes are
  randomly selected on those routes, no
  advertising is done. After a week-long
  experiment, the number of books checked out from
  the twenty bookmobile routes is presented to the
  librarian. The librarian wants to know if the ads
  made any differences in the number of books
  checked out.

3
What kind of statistical test would you use for
the following situations? And why? Identify
independent variable(s) and a dependent variable.

• 2. The city manager of Stone Creek, South
  Dakota, wants to determine if her new personnel
  procedures are decreasing the time it takes to
  hire an employee. She takes a sample of 10 city
  bureaus and calculates the average time to hire
  an employee in days before and after the new
  procedure. The city manager wants to know if the
  new personnel procedures made an impact on the
  time it takes to hire an employee.

4
What kind of statistical test would you use for
the following situations? And why? Identify
independent variable(s) and a dependent variable.

• 3. The police chief wants to know whether the
  citys African-Americans feel that the police are
  doing a good job. In comparison to whites
  evaluations, this information will tell the
  police if they have a community relations problem
  in the African-American community. A survey was
  conducted asking both African-Americans and
  whites in the community to rate the extent to
  which they feel the police is doing a good job. (
  5 point likert scale rating. 1 Not doing a good
  job at all, 5 Doing a very good job.)

5
What kind of statistical test would you use for
the following situations? And why? Identify
independent variable(s) and a dependent variable.

• 4. A professor thinks that the MPA students at
  Portland State University spend more time
  studying than students at University of Portland,
  and Oregon State University. One hundred students
  in MPA program at each university are selected
  and asked to log their studying time during the
  first week of November. A total number of hours
  students spent studying during the first week of
  November is reported back to the professor. The
  professor wants to determine if PSU students
  spent more time studying than other two
  universities.

6
What kind of statistical test would you use for
the following situations? And why? Identify
independent variable(s) and a dependent variable.

• Morgan City uses four types of cars for the city
  automotive fleet Honda Accord, Subaru Legacy,
  Volkswagen Passat, and Chevy Suburban. A City
  Maintenance Chief wants to compare the
  maintenance cost by car types to find out if he
  can cut back the maintenance cost by selecting
  one type that has the least maintenance cost.
  Maintenance cost for all city cars is reported to
  the Maintenance Chief.

7
What kind of statistical test would you use for
the following situations? And why? Identify
independent variable(s) and a dependent variable.

1. The Beaver Dam Job Placement Center wants to
   evaluate the quality of its program. One hundred
   and fifty unemployed individuals are selected at
   random. Fifty of them (randomly selected) went
   through the Beaver Dam Job Placement Centers
   program. Another fifty of them (randomly
   selected) took a job placement workshop offered
   through Beaver Dam Community College. The rest of
   them did not take any job placement program. Six
   months later the income of those 150 individuals
   were surveyed in order to determine the
   effectiveness of the Beaver Dam Job Placement
   Centers program.

8
Review Levenes Test

• Homogeneity Test
• Tests the null hypothesis that the variance of
  the dependent variable is equal across groups.
• If the result of the Levenes Test is
  significant, what does that mean?

9
Review Levenes Test

• When the result of the Levenes Test is
  significant (p lt. 05)
• T-test Equal variances not assumed
• ANOVA Technically speaking, it violates the
  assumption of ANOVA, and therefore, ANOVA should
  not be used.
• (Though the post-hoc test using Dunnets C gives
  you the multiple comparisons of two groups
  adjusting for the significant differences in
  variance).

10
Factorial ANOVA

• T-test and One way ANOVA
• 1 independent variable (e.g. Gender), 1 dependent
  variable (e.g. Test score)
• Two-way ANOVA (Factorial ANOVA)
• 2 (or more) independent variables (e.g. Gender
  and Academic Standing), 1 dependent variable
  (e.g. Test score)

11
Main Effects and Interaction Effects

• Main Effects
• The effects for each independent variable on the
  dependent variable.
• Differences between the group means for each
  independent variable on the dependent variable.
• Interaction Effect
• When the relationship between the dependent
  variable and one independent variable differs
  according to the level of a second independent
  variable.
• When the effect of one independent variable on
  the dependent variable differs at various levels
  of second independent variable.

12
Main Effects and Interaction Effects

• (See Handout)

13
SPSS Demo

• Open carpet.sav
• Analyze
• General Linear Model
• univariate
• Select a dependent variable
• Select independent variables and put it in the
  Fixed Factor box.
• plots
• move the fixed factors to horizontal and
  veritical axes box. Click Add.

14
SPSS Demo

• Click options
• Select the two independent variables and move to
  Display means for box.
• Click Descriptive statistics
• Click Continue then OK

15
Interpretation of the result

• ANOVA table Test of between subject effects
• Main effects? Significant? Whats the F
  statistic? df?
• Interaction effect? Significant? Whats the F
  statistic? df?
• What does that mean in relation to the question
  you are asking?
• Write up your result. (Handout)

16
Chi-Square ? 2 statistics

• Testing if two groups are the same.
• Comparing 2 groups when the dependent variable is
  categorical.
• Remember T test is to compare 2 groups when the
  dependent variable is continuous.

17
Chi-Square ? 2 statistics

• If two variables are statistically independent,
  they are not related at all. (Knowing how a
  person is categorized on one variable provides
  absolutely no hint as to how they might be
  categorized on the other. )
• If two variables are statistically dependent,
  knowing a persons status on one variable is
  useful in predicting their status on the other.

18
Hypothesis

• Test of statistical independence  
• Null Hypothesis the two variables are
  independent.
• Alternative Hypothesis the two variables are
  dependent.

19
Contingency Table
20
Chi-square Formula

• The formula for computing chi-square Gauges how
  closely our observed frequencies in each cell of
  the table are matched to the expected
  frequencies.
• Oi stands for the observed frequency in one cell.
  
• Ei stands for the expected frequency of that
  cell.
• As you can see in the formula, we compute
  chi-square by summing up the differences between
  the observed and the expected frequency for each
  cell.

21
Reject or Retain the Null Hypothesis

• The more dependent the two variables are in the
  sample, the larger the chi-square statistic would
  be. If the statistic is large enough it would
  exceed the critical value associated with a
  selected alpha level (in other words, if p lt.05)
  then
• Reject the Null hypothesis of independence (no
  relation between the two variables)
• Conclude that the two variables are statistically
  dependent (related).

22
Example of Chi-square analysis
23
SPSS Demo