Contingency Tables
A contingency table is a two-way table that is used to explain the nature of relationships between two or more categorical variables. The table’s cells contain frequencies or counts corresponding to the variables under comparison. A contingency table is an ideal form of an experiment that aims at explaining in details the relationship between two categorical variables. An example of a contingency table is one showing the relationship between the gender and smoking status of adults. Gender of the adults has the values male and female while the smoking status has the values smoker and nonsmokers. There is a perception that there exist significant differences in the smoking status of individuals based on gender making this experiment using the contingency table appropriate in in-depth explaining of the presumed relationships. The table corresponding to the thought experiment is expressed in the form of frequencies for both the values of gender and smoking status. A hypothetical group of 120 males and 100 females is used to construct a hypothetical contingency table shown below;
Gender Smoker Non-smoker Total
Male 70 50 120
Female 30 70 100
Total 100 120 220

The cause factor in this table is the gender while the effect variable is the smoking status. The first row represents the male gender, and it shows that 70 of the 120 males are smokers while 50 of the 120 males are non-smokers. This implies that 58% of the males are smokers while 42% are non-smokers. The second row represents the female gender, and it shows that 30 of the 100 females are smokers while 70 of the 100 females are non-smokers. This implies that 30% of the females are smokers while 70% are non-smokers. The hypothetical contingency table reveals the following theoretical interpretation; Males are more likely to be smokers compared to women because the percentages corresponding to this are more in the male’s category compared to the female gender hence making the theoretical statement appropriate.
Scatterplots
The scatterplots are visual tools used to elucidate the nature of the relationship existing between pairs of variables. The scatterplots shown below indicates the relationship between the student’s performance in the form of GPA with the days of attendance in class as well as involvement in games and sports;
Figure1: negative association (Inverse relationship curve) scatterplot
The following is the data corresponding to this plot;

The scatterplot corresponds to this data;

Figure2: Positive relationship scatterplot

The first scatterplot indicates a negative or inverse association because the line moves from top left to bottom right which is the ideal characteristic of an inverse relationship which implies that the correlation between the GPA and the corresponding grades of the students are not significant even if the association is negatively linear. This implies that the games played are not directly proportional to the performance of the students. The second scatterplot indicates a positive association because the line moves from bottom left to top right which is the ideal characteristic of significant positive relationship which implies that the relationship between the GPA and the class attendance in days are significant because the association is positively linear.

References
Jaccard, J., & Jacoby, J. (2009). Theory construction and model-building skills: A practical guide for social scientists. Guilford Press.
Fagerland, M., Lydersen, S., & Laake, P. (2017). Statistical analysis of contingency tables. Chapman and Hall/CRC.