Analyzing Data: Bivariate Relationships

1
Analyzing Data Bivariate Relationships

• Chapter 7

2
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

3
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 gt groups need to 100

4
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 gt Tables
  gt Cross Tabulation

5
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 gt Basic Statistics gt Correlation

6
Interval/Ratio Variables

• Scatterplots are most common for presenting
  interval/ratio variables
• You have choices
• Just a basic plot Select Graph gt Plot
• Fitted line plot Select Stat gt Regression gt
  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.

7
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