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Analyzing Data: Bivariate Relationships

This chapter covers how to analyze bivariate relationships in data. Learn how to label variables, present data, and select relevant statistics. Topics include contingency tables, testing bivariate relationships, correlation, and presenting interval/ratio variables.

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Analyzing Data: Bivariate Relationships

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  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 > 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 > Tables > 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 > Basic Statistics > Correlation

  6. 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.

  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

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