Bivariate Data
Bivariate data refers to a set of data that involves two different variables. In mathematical terms, it represents pairs of observations or measurements for two different characteristics or factors. Analyzing bivariate data allows for the exploration of relationships and patterns between the two variables, often through methods such as scatter plots and correlation analysis.
8 Key excerpts on "Bivariate Data"
eBook - ePubUnderstanding Research Methods
A Guide for the Public and Nonprofit Manager
- Donijo Robbins(Author)
- 2017(Publication Date)
- Routledge(Publisher)
...Chapter 11 Bivariate Statistics 11.1 Introduction Once researchers have described single variables using univariate statistics, they may delve deeper into additional analyses. That is, researchers may examine the relationship between two or more variables. When investigating the relationship between two variables, researchers are performing a bivariate analysis, whereas they are conducting a multivariate analysis when three or more variables are studied. This chapter focuses on bivariate analyses—studying two variables. Multivariate analyzes are more complex, and as such are beyond the scope of this book. In fact, the majority of the statistical techniques preferred by practitioners are simple univariate and bivariate analysis—those discussed in the previous chapter and presented in this chapter. Similar to univariate statistics, the type of data drives the manner in which the two variables are analyzed; different types of analyses require different types of data. The purpose of this chapter is to illustrate four different, but very simple and popular, bivariate statistical procedures: cross tabulations, difference of means, analysis of variance, and correlations. Each of these procedures tests a supposition (i.e., hypothesis) by examining a relationship or an association between two variables, usually an independent and a dependent variable. Before discussing these different procedures, we briefly review the process of testing relationships. 11.2 Testing for Relationships A researcher can look at the univariate statistics of two variables or their respective graphs and claim a relationship exists; however, they cannot say, beyond a reasonable doubt, that a relationship exists without testing for the statistical significance of a relationship. The statistical test is only one of the criteria researchers use to help support cause and effect...
eBook - ePubDoing Survey Research
A Guide to Quantitative Methods
- Peter M. Nardi(Author)
- 2018(Publication Date)
- Routledge(Publisher)
...7 Analyzing Data Bivariate Relationships The invalid assumption that correlation implies cause is probably among the two or three most serious and common errors of human reasoning. —Stephen Jay Gould, scientist Learning Goals Understanding bivariate statistical analysis is the focus of this chapter. Central to this is learning how to read and construct cross-tables of data and deciding which statistics to use to measure association and correlation (see Figure 7.1). By the end of the chapter, you should understand how to reject or accept a hypothesis using the appropriate statistics to assess bivariate relationships. You should also be able to put together cross-tables and interpret them clearly in words. Figure 7.1 Statistical Decision Steps (also see Statistical Analysis Decision Tree in Appendix) After you evaluate your univariate data analysis and feel confident that you have variables with good distributions, it is now time to begin investigating the bivariate relationships you proposed in your research questions and hypotheses. Bivariate Data analysis assesses the association between two variables. If you are interested in studying three or more variables at a time, then multivariate analysis is required (see Chapter 9). Remember, if for some reason any of your variables approximate a constant—that is, almost everyone has selected only one or two of the values for that variable—then you must eliminate them from further analysis. For example, when 90 percent of the people who completed the questionnaire agree or strongly agree that they are satisfied with their current job, then job satisfaction may no longer be a variable in your study unless the sample size is very large. Keep in mind what the objective is: to demonstrate whether the independent variable is exerting significant influence on the dependent variable in order to infer something about a population from which your sample was selected...
eBook - ePub- Clive Seale, Clive Seale(Authors)
- 2017(Publication Date)
- SAGE Publications Ltd(Publisher)
...21 Bivariate analysis Clive Seale Chapter contents Contingency tables 362 Statistical significance 364. . Chi-squared test for contingency tables 365. . Other ways of testing for significance 366 Measures of association 367 Using interval variables 367. . Scattergrams, correlation and regression 367. . Comparing the means of two groups 370 Conclusion 372 Univariate analysis can show us how a single group of people varies on some characteristic, such as sex, age or job satisfaction. However, to really understand data and to think about it theoretically or in terms of policy development or evaluation, it is necessary to explore the relationship between two or more variables. Bivariate analysis involves the exploration of relationships between two variables. For instance, a researcher might seek to discover the relationship between gender and fear of crime, or between country of origin and levels of spoken English, or age and health status. Where the researcher is concerned with the relationship between three or more variables, multivariate statistics are used, covered in the next chapter, which also shows how statistical reasoning can be used to construct arguments about causality, the idea that one variable has caused another variable to vary. For the moment though, let us just deal with two variables at a time. Contingency tables A good way to approach bivariate analysis, as long as the variables involved do not have too many categories, is through the analysis of contingency tables...
eBook - ePubQuantitative Data Analysis with Minitab
A Guide for Social Scientists
- Alan Bryman, Duncan Cramer(Authors)
- 2003(Publication Date)
- Routledge(Publisher)
...Chapter 8 Bivariate analysis Exploring relationships between two variables This chapter focuses on relationships between pairs of variables. Having examined the distribution of values for particular variables through the use of frequency tables, histograms, and associated statistics as discussed in Chapter 5, a major strand in the analysis of a set of data is likely to be bivariate analysis— how two variables are related to each other. The analyst is unlikely to be satisfied with the examination of single variables alone, but will probably be concerned to demonstrate whether variables are related. The investigation of relationships is an important step in explanation and consequently contributes to the building of theories about the nature of the phenomena in which we are interested. The emphasis on relationships can be contrasted with the material covered in the previous chapter, in which the ways in which cases or subjects may differ in respect to a variable were described. The topics covered in the present chapter bear some resemblance to those examined in Chapter 7, since the researcher in both contexts is interested in exploring variance and its connections with other variables. Moreover, if we find that members of different ethnic groups differ in regard to a variable, such as income, this may be taken to indicate that there is a relationship between ethnic group and income. Thus, as will be seen, there is no hard-and-fast distinction between the exploration of differences and of relationships. What does it mean to say that two variables are related? We say that there is a relationship between two variables when the distribution of values for one variable is associated with the distribution exhibited by another variable. In other words, the variation exhibited by one variable is patterned in such a way that its variance is not randomly distributed in relation to the other variable...
eBook - ePubQuantitative Data Analysis with SPSS 12 and 13
A Guide for Social Scientists
- Alan Bryman, Duncan Cramer(Authors)
- 2004(Publication Date)
- Routledge(Publisher)
...Chapter 8 Bivariate analysis: exploring relationships between two variables Crosstabulation Crosstabulation and statistical significance: the chi-square (χ2) test Correlation Other approaches to bivariate relationships Regression Overview of types of variable and methods of examining relationships Exercises T HIS CHAPTER FOCUSES on relationships between pairs of variables. Having examined the distribution of values for particular variables through the use of frequency tables, histograms, and associated statistics as discussed in Chapter 5, a major strand in the analysis of a set of data is likely to be bivariate analysis – how two variables are related to each other. The analyst is unlikely to be satisfied with the examination of single variables alone, but will probably be concerned to demonstrate whether variables are related. The investigation of relationships is an important step in explanation and consequently contributes to the building of theories about the nature of the phenomena in which we are interested. The emphasis on relationships can be contrasted with the material covered in the previous chapter, in which the ways in which cases or subjects may differ in respect to a variable were described. The topics covered in the present chapter bear some resemblance to those examined in Chapter 7, since the researcher in both contexts is interested in exploring variance and its connections with other variables. Moreover, if we find that members of different ethnic groups differ in regard to a variable, such as income, this may be taken to indicate that there is a relationship between ethnic group and income. Thus, as will be seen, there is no hard-and-fast distinction between the exploration of differences and of relationships. What does it mean to say that two variables are related? We say that there is a relationship between two variables when the distribution of values for one variable is associated with the distribution exhibited by another variable...
eBook - ePubStats Means Business
Statistics and Business Analytics for Business, Hospitality and Tourism
- John Buglear(Author)
- 2019(Publication Date)
- Routledge(Publisher)
...Correlation analysis enables us to assess whether there is a connection between the two variables and, if so, how strong that connection is. If correlation analysis tells us there is a connection, we can use regression analysis to identify the exact form of the relationship. It is essential to know this if you want to use the relationship to make predictions, for instance if we want to predict the demand for ice cream when the daily temperature is at a particular level. The assumption that underpins bivariate analysis is that one variable depends on the other. The letter Y is used to represent the dependent variable, the one whose values are believed to depend on the other variable. This other variable, represented by the letter X, is called the independent variable. The Y or dependent variable is sometimes known as the response because it is believed to respond to changes in the value of the X. The X or independent variable is also known as the predictor because it might help us to predict the values of Y. 4.2.1 Correlation analysis Correlation analysis is a way of investigating whether two variables are correlated, or connected with each other. We can study this to some extent by using a scatter diagram to portray the data, but such a diagram can only give us a visual ‘feel’ for the association between two variables; it doesn’t actually measure the strength of the connection. So, although a scatter diagram is the thing you should begin with to carry out bivariate analysis, you need to calculate the correlation coefficient – the Pearson correlation coefficient, to be precise – if you want an accurate way of assessing how closely the variables are related. The correlation coefficient is similar to the standard deviation in that it is based on the idea of dispersion or spread...
eBook - ePubQuantitative Data Analysis with IBM SPSS 17, 18 & 19
A Guide for Social Scientists
- Alan Bryman, Duncan Cramer(Authors)
- 2012(Publication Date)
- Routledge(Publisher)
...Chapter 8 Bivariate analysis: exploring relationships between two variables ■ Crosstabulation ■ Crosstabulation with statistical significance: the chi-square (χ 2) test ■ Correlation ■ Other approaches to bivariate relationships ■ Regression ■ Overview of types of variable and methods of examining relationships ■ Exercises T HIS CHAPTER FOCUSES on relationships between pairs of variables. Having examined the distribution of values for particular variables through the use of frequency tables, histograms, and associated statistics as discussed in Chapter 5, a major strand in the analysis of a set of data is likely to be bivariate analysis – how two variables are related to each other. The analyst is unlikely to be satisfied with the examination of single variables alone, but will probably be concerned to demonstrate whether variables are related. The investigation of relationships is an important step in explanation and consequently contributes to the building of theories about the nature of the phenomena in which we are interested. The emphasis on relationships can be contrasted with the material covered in the previous chapter, in which the ways in which cases or participants may differ in respect to a variable were described. The topics covered in the present chapter bear some resemblance to those examined in Chapter 7, since the researcher in both contexts is interested in exploring variance and its connections with other variables. Moreover, if we find that members of different ethnic groups differ in regard to a variable, such as income, this may be taken to indicate that there is a relationship between ethnic group and income...
eBook - ePub- Debbie L. Hahs-Vaughn(Author)
- 2016(Publication Date)
- Routledge(Publisher)
...Chapter 2 Univariate and Bivariate Statistics Review Chapter Outline 2.1 Fundamental Concepts 2.1.1 Hypothesis Testing 2.1.2 Types of Decision Errors 2.1.3 Statistical Versus Practical Significance 2.2 Foundational Univariate Statistics 2.2.1 Histogram 2.2.2 Box-and-Whisker Plot 2.2.3 Scatterplot 2.2.4 Measures of Central Tendency 2.2.5 Measures of Dispersion 2.3 Foundational Bivariate Statistics 2.3.1 Independent and Dependent Samples t Test 2.3.2 Analysis of Variance 2.3.3 Two-Factor ANOVA 2.3.4 Covariance 2.3.5 Pearson Product-Moment Correlation Coefficient 2.3.6 Simple Linear Regression Key Concepts Covariance Correlation Effect size Distributional shape Graphical representation Hypothesis test Power Tests of means Tests of relationships Type I and Type II errors By this point in your quantitative statistics career, you’ve been introduced to a large number of inferential statistics procedures, and you are likely quite comfortable with concepts such as hypothesis testing, significance, power, and similar, as well as procedures to test mean differences and relationships. Nonetheless, it does not hurt to have a brief review of some common univariate and bivariate statistics, as the concepts behind them and the statistics themselves are the foundation for multivariate statistics. We’ll begin with a refresher on a number of basic fundamental concepts, and then touch on a few foundational univariate and bivariate statistics. The goal is that, by the end of this chapter, you will be refreshed on a number of basic concepts that are important as we move into multivariate statistics. 2.1 Fundamental Concepts This section is not meant to serve as either a comprehensive review or an exhaustive summary of fundamental concepts in quantitative statistics...
