Review: T test vs. ANOVAWhen 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.

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

1. 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.

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.

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 city’s 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.)

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.

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

5. 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.

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

6. 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 Center’s 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 Center’s program.

Review: Levene’s Test Homogeneity Test Tests the null hypothesis that the variance of the dependent variable is equal across groups. If the result of the Levene’s Test is significant, what does that mean?

Review: Levene’s Test When the result of the Levene’s Test is

significant (p <. 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 Dunnet’s C gives you the multiple comparisons of two groups adjusting for the significant differences in variance).

Factorial ANOVAT-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)

Example of Factorial ANOVA

Does the type of curriculum and students’ preference for instructional materials affect students’ test scores?

DV Students’ test scores

IV Type of curriculum

Students’ preference for instructional materials

Example of Factorial ANOVA

Does the consumers’ carpet rating differ depending on the packaging type and the brand name?

DV Consumer’s carpet rating

IV Packaging type

Brand name

Example of Factorial ANOVA

Does the employee’s starting salary differ depending on their job type and their gender?

DV Employee’s starting salary

IV Job type

Gender

Example of Factorial ANOVA

Using your own research project, come up with an example where you can use a Factorial ANOVA for your analysis. Identify the dependent variable and independent variables.

DV

IV

Main Effects and Interaction Effects

Main EffectsThe 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.

Main Effects and Interaction Effects

(See Handout)

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”.

SPSS Demo Click “options” Select the two independent variables

and move to “Display means for” box.

Click “Descriptive statistics” Click “Continue” then “OK”

Interpretation of the result ANOVA table = Test of between subject effects

Main effects? Significant? What’s the F statistic? df?Interaction effect? Significant? What’s the F statistic? df?

What does that mean in relation to the question you are asking?

Write up your result. (Handout)

Chi-Square 2 statisticsTesting 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.

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 person’s status on one variable is useful in predicting their status on the other.

Hypothesis Test of statistical independence  

Null Hypothesis: the two variables are independent.

Alternative Hypothesis: the two variables are dependent.

Contingency Table

Females Males Total

Democrats 50 70 120

Republicans 19 41 60

Total 69 111 180

Chi-square: FormulaThe 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.

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 <.05) then:

Reject the Null hypothesis of independence (no relation between the two variables)

Conclude that the two variables are statistically dependent (related).

Example of Chi-square analysis

SPSS Demo