Analyzing Data Bivariate Relationships Chapter 7 Getting Starting

Analyzing Data: Bivariate Relationships Chapter 7

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

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

Testing Bivariate Relationships n Assessing relationships between nominal and ordinal measures is done via chi-square n Can be used to test the independence of the row and column variables in a two-way table. n 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. n To perform this in Minitab, Select: Stat > Tables > Cross Tabulation

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

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

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