Q1 Null Hypothesis and Answers
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-statistic
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 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: 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 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: 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.