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