Q1 Study Guide Null Hypothesis

There are the three types of studies

Relationship study, Differences study, Non-parametric study

These are the three null hypotheses for the three types of studies 

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)

These are the common statistical procedures you will learn, each one has a specific data-type combination

 Pearson r

Bivariate Regression

One-sample t-test

Independent-sample t-test

Paired sample t-test

Analysis of Variance (ANOVA)

One-way Chi-square X2

Two-way Chi-square X2

1.  Metric / Metric  Independent variable is metric

    Dependent variable is 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.

Study type / statistical procedure: 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”) 

Theory:  More Education results in less serious offenses

Null hypothesis: There is not a statistically significant relationship between severity of offense and education.

Study type / statistical 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:  Income of members in the "treated" sample is higher than the population of persons in that County

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

 Study type / statistical procedure: Differences study / one-sample t-est

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

The difference in mean crimes between two neighborhood-demographic)

Theory:  Crime is 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.

Study type / statistical procedure: Differences study / independent t-test (with two groups).

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: Scores will be higher after the treatment

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

Study type / statistical procedure: Differences study / paired sample t-test.   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:  Income of Caucasians will be higher than that of persons of color. 

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

Study type / statistical procedure: 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 students at a given university.

Theory: More females than males in 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.

 Study type / statistical procedure: 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: Males vote Republican, Females vote Democrat

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.

Study type / statistical procedure: 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.