Analyzing Data: Bivariate Relationships Chapter 7

Getting Starting Label each variable in your study as nominal, ordinal, or interval/ratio Decide how you will present the data Select the most relevant statistics

Contingency Tables Often referred to as cross tabs Study two variables simultaneously Best for nominal or ordinal Interval/ratio if very few categories Size of table is defined as Row X Column Independent variable = column Dependent variable = row Cells: intersections of rows and columns When making comparisons > groups need to = 100%

Testing Bivariate Relationships Assessing relationships between nominal and ordinal measures is done via chi-square Can be used to test the independence of the row and column variables in a two-way table. Use the chi-square statistic (goodness-of-fit) to accept or reject the null hypothesis that the frequency of observed values is the same as the expected frequency. To perform this in Minitab, Select: Stat > Tables > Cross Tabulation

Correlation Pearson product moment correlation coefficient measures the degree of linear relationship between two variables. The correlation coefficient has a range of -1 to 1. If one variable tends to increase as the other decreases, the correlation coefficient is negative. If the two variables tend to increase together the correlation coefficient is positive. For a two-tailed test of the correlation H0: r = 0 versus HA: r 0 where r is the correlation between a pair of variables. Select: Stat > Basic Statistics > Correlation

Interval/Ratio Variables Scatterplots are most common for presenting interval/ratio variables You have choices Just a basic plot – Select: Graph > Plot Fitted line plot – Select: Stat > Regression > Fitted line plot Minitab calculates a Pearson correlation coefficient. If the distribution fits the data well, then the plot points will fall on a straight line.

Purposes of Measuring Relationships Main goals of research Describe Explain Predict Three main purposes To account for why the dependent variable varies among respondents To predict future occurrences Describe relationships among variables