Directions:

Determine what the appropriate statistical test is for your main two variables of interest. Your options are:

- Analysis of variance (ANOVA) assesses whether the means of two or more groups are statistically different from each other. This analysis is appropriate whenever you want to compare the means (quantitative variables) of groups (categorical variables). The null hypothesis is that there is no difference in the mean of the quantitative variable across groups (categorical variable), while the alternative is that there is a difference.
- A Chi-Square Test of Independence compares frequencies of one categorical variable for different values of a second categorical variable. The null hypothesis is that the relative proportions of one variable are independent of the second variable; in other words, the proportions of one variable are the same for different values of the second variable. The alternate hypothesis is that the relative proportions of one variable are associated with the second variable. Note: although it is possible to run large Chi-Square tables (e.g. 5 x 5, 4 x 6, etc.), the test is really only interpretable when you response variable has 2 levels (see Graphing decisions flow chart in bivariate graphing chapter).
- Correlation coefficient assesses the degree of linear relationship between two variables. It ranges from +1 to -1. A correlation of +1 means that there is a perfect, positive, linear relationship between the two variables. A correlation of -1 means there is a perfect, negative linear relationship between the two variables. In both cases, knowing the value of one variable, you can perfectly predict the value of the second. Note: Two 3+ level categorical variables can be used to generate a correlation coefficient if the the categories are ordered and the average (i.e. mean) can be interpreted. The scatter plot on the other hand will not be useful. In general the scatterplot is not useful for discrete variables (i.e. those that take on a limited number of values). When we square r, it tells us the proportion of the variability in one variable that is described by variation in the second variable (aka RSquare or Coefficient of Determination).
- Please note: If you have a quantitative explanatory variable and a categorical response, you will eventually be using logistic regression. For now, categorize your explanatory variable and use a chi-square test as explained above.

The requirement of this assignment is to: Run the appropriate test, post the syntax used, and interpret your findings. In addition, use post-hoc tests if appropriate. Please see the samples below for guidance in writing statistical findings.

**Sample Submission: **

- Example of how to write results for ANOVA:
- When examining the association between current number of cigarettes smoked (quantitative response) and past year nicotine dependence (categorical explanatory), an Analysis of Variance (ANOVA) revealed that among daily, young adult smokers (my sample), those with nicotine dependence reported smoking significantly more cigarettes per day (Mean=14.6, s.d. ±9.15) compared to those without nicotine dependence (Mean=11.4, s.d. ±7.43), F(1, 1313)=44.68, p=.0001.
- Post hoc ANOVA results: ANOVA revealed that among daily, young adult smokers (my sample), number of cigarettes smoked per day (collapsed into 5 ordered categories, which is the categorical explanatory variable) and number of nicotine dependence symptoms (quantitative response variable) were significantly associated, F (4, 1308)=11.79, p=.0001. Post hoc comparisons of mean number of nicotine dependence symptoms by pairs of cigarettes per day categories revealed that those individuals smoking more than 10 cigarettes per day (i.e. 11 to 15, 16 to 20 and >20) reported significantly more nicotine dependence symptoms compared to those smoking 10 or fewer cigarettes per day (i.e. 1 to 5 and 6 to 10). All other comparisons were statistically similar.

- Chi-Square Test of Independence
- When examining the association between lifetime major depression (categorical response) and past year nicotine dependence (categorical explanatory), a chi-square test of independence revealed that among daily, young adults smokers (my sample), those with past year nicotine dependence were more likely to have experienced major depression in their lifetime (36.2%) compared to those without past year nicotine dependence (12.7%), X2 =88.60, 1 df, p=0001.
- Post hoc Chi-Square results: A Chi Square test of independence revealed that among daily, young adult smokers (my sample), number of cigarettes smoked per day (collapsed into 5 ordered categories) and past year nicotine dependence (binary categorical variable) were significantly associated, X2 =45.16, 4 df, p=.0001. Post hoc comparisons of rates of nicotine dependence by pairs of cigarettes per day categories revealed that higher rates of nicotine dependence were seen among those smoking more cigarettes, up to 11 to 15 cigarettes per day. In comparison, prevalence of nicotine dependence was statistically similar among those groups smoking 10 to 15, 16 to 20, and > 20 cigarettes per day.
- For an example when response variable is categorical with more than 2 levels, please refer to document (Additional Sample Result Write – Chi Square).

- Correlation
- Among daily, young adult smokers (my sample), the correlation between number of cigarettes smoked per day (quantitative) and number of nicotine dependence symptoms experienced in the past year (quantitative) was 0.17 (p=.0001), suggesting that only 3% (i.e. 0.17 squared) of the variance in number of current nicotine dependence symptoms can be explained by number of cigarettes smoked per day.