Q1 Study Guide SP 25

Study Guide:  The Null Hypothesis for differing Data-type combinations

These are the three null hypotheses for three common study-designs

1.  The relationship null hypothesis (used with a metric-metric data-type combination)

2.  The differences null hypothesis (used with a metric-nominal data-type combination)

3.  The non-parametric null hypothesis (used with a nominal-nominal data-type combination)

Sample Problem:   

1.  Metric / Metric  Independent variable --  Dependent variable =  metric

Example: the effect of additional police on crime

Theory:  Adding police to a neighborhood will affect the number of crimes (Police go up, crimes go down)

Null hypothesis: There is not a statistically significant relationship between the number of crimes reported and the number of police present.  Either (p. < .05) or (p. > .05), if the relationship is statistically significant. Reject the null.

Study type / test statistic: Relationship study / Pearson r statistic.

2. Metric / Metric (Prediction)

Education will predict the seriousness of offenses among those who commit crimes.  (Predict the “seriousness of the offense” by the number of “years of education”) 

Test the Null hypothesis: There is not a statistically significant relationship between severity of offense and education. Then (if the relationship is statistically significant) reject the null and use the independent variable (education) as a predictor of crime severity.

Study type / Procedure: Relationship Study / Bivariate Regression

3.  Nominal / Metric (One Sample mean compared to the population mean)

The difference in mean income between the population and a sample neighborhood from that population. 

Theory:   The sample neighborhood has lower income than the population.

Null hypothesis: There is not a statistically significant difference in mean income between residents in Multicultural Neighborhood and residents in the county population.

 Either (p. < .05) or (p. > .05), if the difference is statistically significant, reject the null.

Study type / test statistic: Differences study / one-sample t-statistic. Ascertain if the obtained t is significant.

4.  Nominal / Metric  (Comparing two “independent” sample means) 

The difference in mean crimes between two neighborhood-demographic)

Theory:  Crimes are lower in Caucasian Neighborhoods than in multicultural neighborhoods.

Null hypothesis: There is not a statistically significant difference in mean crimes between Caucasian  neighborhoods and multicultural neighborhoods.

Either (p. < .05) or (p. > .05), if the difference is statistically significant, reject the null.

Study type / test statistic: Differences study / independent t statistic (with two groups). Ascertain if the obtained t is significant.

5.  Nominal / Metric (paired sample)  “observation at two different times”  the dependent variable is metric

The difference between the mean pretest score and the mean posttest score of a treatment that was intended to raise the posttest scores). 

Theory:  GPA will be higher after the study skills class.

Null hypothesis: There is not a statistically significant difference in mean GPA between pre-treatment and post-treatment.

 Either (p. < .05) or (p. > .05), if the difference is statistically significant, reject the null.

Study type / test statistic: Differences study / paired sample t statistic.   Ascertain if the obtained t is significant.

6.  Nominal / Metric (Independent variable with more than two groupings)

 The difference in mean income between Latinos, Caucasians, and African Americans). 

Theory:  Mean income is different according to race, between Latinos, Caucasians, and African Americans

Null hypothesis: There is not a statistically significant difference in mean income between Latinos, African Americans, and Caucasians.

Either (p. < .05) or (p. > .05), if the difference is statistically significant, reject the null.

Study type / test statistic: Differences study / Analysis of Variance (ANOVA) Testing the means of 3 or more groups. Ascertain if the obtained F is significant.

7.  Nominal - Count There is one nominal independent variable with two levels, the dependent variable is the number of frequencies in each level (called count-data). 

The difference in the number of male and female students at a given university.

Theory:  There are more females attending college.

Null hypothesis: There is not a statistically significant difference in the number of students, among males and females, between the observed count and the expected count.

 (p. < .05), the difference is significant. Reject the null. 

Study type / test statistic: Non-parametric differences study / one-way chi-square statistic.  Ascertain if the obtained X2 is significant.

8.  Nominal - Nominal - Count There is a nominal independent variable, and a nominal dependent variable (the dependent variable is frequencies in a designated level -- count data).

The difference in the number of republicans and democrats among males and females.

Theory:  The democrat (liberal) ideology attracts females in greater number over males.

Null hypothesis: There is not a statistically significant difference in the number of democrats among males and females between the observed count and the expected count.

 (p. < .05), the difference is significant. Reject the null.

Study type / test statistic: Non-parametric differences study / Two-way chi-square statistic.  Ascertain if the obtained X2 is significant. It examines the occurrences among two levels of a nominal dependent variable based on two levels of a nominal independent variable.