Bivariate Relationships: Analyzing Contingency Tables and Correlations, Slides of Research Methodology

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Analyzing Data: Bivariate Relationships

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

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

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