## Chapter 16 - Quantitative Analysis

Explore this chapter's resources further:**Educational objectives**

After completing this chapter, you will:

- have an understanding of the nature, types and purpose of tables and graphs as employed in quantitative research;
- have gained clear knowledge of the measures of central tendency, dispersion, correlations, and significance;
- be in a position to choose the right tests as required by the nature of the variables in question;
- have gained the skills required to compute correlations and interpret the results of such computations using computers;
- have acquired a critical understanding of the limitations of these tests and their place in social research.

### Contents

- Steps of data analysis
- Presentation of grouped data
- Statistical processing
- Associations
- Tests of significance

### Points to remember

The following are the major points introduced in this chapter. Ensure that you are very confident with their meaning, content, context and significance.- Tables and graphs are the most popular methods of data presentation in qualitative research.
- Table presentation is expected to adhere to rules of clarity, simplicity, economy of space, order of variables, appearance, accuracy and objectivity.
- Graphs present data visually. Most graphs are constructed within the framework of the coordinate axes; the X-axis (abscissa) and the Y-axis (ordinate).
- A mean describes the central trend or average of all observations.
- Mode is the category of a distribution that has the largest number of observations.
- Median is the point on a distribution that divides the observations (not their values) into two equal parts.
- The variance is the average of the squared deviations from the mean.
- Standard deviation is the square root of the variance.
- The range describes the distance between the lowest and the highest score in a distribution.
- Correlations display the relationship between two variables.
- Correlation coefficients demonstrate the presence or absence of correlation, the direction of correlation and the strength of correlation.
- A correlation coefficient ranges from +1 to â€“1.
- Spearman's rho and Pearson's r are the most commonly used measures of association.
- Spearman's rank order correlation coefficient is employed when data are ordinally measured.
- Pearson's rank order correlation coefficient is suitable for interval/ratio measured data.
- A positive correlation means that when one variable is increased the other will increase too.
- A negative correlation indicates that an increase in one variable is associated with a decrease in the other.
- A zero correlation means that there is no association between the variables.
- The coefficient of determination is the square of the coefficient of correlation and displays the degree of variability shared by the two variables.
- Tests of significance relate statistics to parameters; the sample to the target population; the study to the society.
- Parametric tests assume that the variable in question is normally distributed in the population; they employ the normal curve.
- Non-parametric tests do not assume that the variable is normally distributed in the population.
- Tests of significance work around the notion of null hypothesis (Ho): if the significance level of a particular test is below .05, the Ho is rejected; if it is above .05, the Ho is accepted.
- The most common tests of significance are chi-square test, t-test and analysis of variance.
- Chi-square tests are suitable for nominal data; t-tests and ANOVA are suitable for interval/ratio level data.
- The t-test and ANOVA compare means rather than scores. They answer the question whether the differences between the means are significant or not.
- Computer programs such as SPSS can assist with computing significance tests, making relevant computations and conclusions fast, precise and easy.

### Short-answer questions

Answer each question carefully (there is no need to write down the answer). Consult your Social Research text when your memory fails you or when you are in doubt about the accuracy of your responses.- Describe briefly the main points of the process of quantitative analysis.
- How are computers employed in quantitative research and for what purpose?
- What are the advantages of using computers in social research?
- What does the process of data preparation involve in quantitative analysis?
- Explain how coding helps prepare data for quantitative analysis.
- Describe the process of processing open-ended questions for analysis.
- Describe briefly the process of counting and tallying as elements of quantitative analysis.
- What are the main measures of central tendency employed in social research?
- What are the main properties of the mean, median and mode?
- When are the mean, the median and the mode employed?
- Which of the three measures of central tendency is the most effective?
- Describe briefly the nature and purpose of the measures of dispersion.
- Define variance and standard deviation and explain their purpose for social research.
- Describe briefly the nature and purpose of correlation.
- What are the major types of correlation measures employed in social research?
- What are the measures of association that are suitable for nominal, ordinal and interval/ratio data?
- When is Spearman's rho employed?
- When and under what conditions is Pearson's r employed?
- How are correlation coefficients interpreted?
- What are tests of significance and what is their purpose?
- What is a one-tailed and what is a two-tailed test?
- What are parametric and what non-parametric tests?
- What are the major significance tests that are suitable for nominal-level data?
- What are chi-square tests and what is their purpose?
- What is characteristic about the t-test, when is it employed and how are the findings interpreted?
- What are the types of t-tests and when are they used in social research?
- Explain the purpose of ANOVA test and the way in which F is interpreted.
- What are the major differences between t-test and ANOVA?
- What are the major conditions for the application of ANOVA?
- List five differences between quantitative and qualitative analysis.

### Fill-in questions

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