Primary Data Analysis

Preparing for Quantitative Data Analysis

In general, quantitative research attempts to find either differences or relationships. A researcher must formulate a limited list of primary hypotheses or research questions in advance to keep the research project within a manageable scope. Each hypothesis or research question includes clearly specified variables. As comparison hypotheses predict differences among categories or groups, the independent variables are generally categorical, whereas, as relationship hypotheses predict relationships between theoretically related constructs, the independent variables are generally continuous. In most cases, dependent variables are continuous.

Once hypotheses and research questions are developed, a research study is designed to collect numerical data, or raw data, from a sample of participants that are randomly drawn from a population. When experiments are used, the researcher typically randomly assigns participants to conditions. When random sampling or assignment is not possible, the researcher describes how the deviation of the actual research design from the intended research design may affect the results and discuss both strengths and limitations of the study. The raw data are then compiled into a data set to be analyzed using statistical software programs, such as SPSS or SAS. Two types of statistics are needed to answer research questions or test hypotheses: descriptive and inferential statistics.

Descriptive Statistics

Descriptive statistics are used to summarize responses from a sample and characterize that sample. Researchers collect a large amount of data, and to make sense of the data, they need to organize and simplify data in a sensible way. Researchers describe data for each quantitative variable in three ways: the number of cases or data points, central tendency (how the majority of participants respond to a variable), and dispersion or variability (how participants’ scores are spread out from the point of central tendency).

There are three measures of central tendency: mean, median, and mode. The mean is the arithmetic average computed by summing the values of all the observations and dividing by the total number of observations. The median refers to the middle of all the rank-ordered scores on a given variable, and the mode is the score that appears most often in a data set.

To fully describe a distribution of data, knowing where the middle is located is not enough. Two distributions can have the same mean but different spreads of scores (the greater spreads, the larger the standard deviations). Likewise, they can have the same median but different ranges. Therefore, standard deviation (SD) and range, the two most commonly reported measures of dispersion, often accompany the measures of central tendency in quantitative research reports. For interval or ratio data that follow an approximately normal curve, means and SDs are commonly reported; in theory, 68.26% of the cases in a data set fall within the −1 and +1 SD, 95.44% fall within −2 and +2 SDs, and 99.72% fall within −3 and +3 SDs. For skewed distributions, the median, mode, and range are considered more appropriate, whereas for nominal data, frequencies and proportions, such as the number and proportion of males and females, are commonly reported.

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