The following module provides an overview of quantitative data analysis, including a discussion of the necessary steps and types of statistical analyses.
- List the steps involved in analyzing quantitative data
- Define and provide examples of descriptive statistical analyses
- Define and provide examples of inferential statistical analyses
Quantitative studies result in data that provides quantifiable, objective, and easy to interpret results. The data can typically be summarized in a way that allows for generalizations that can be applied to the greater population and the results can be reproduced. The design of most quantitative studies also helps to ensure that personal bias does not impact the data. Quantitative data can be analyzed in several ways. This module describes some of the most commonly used quantitative analysis procedures.
The first step in quantitative data analysis is to identify the levels or scales of measurement as nominal, ordinal, interval or ratio. See the Research Ready: Scales of Measurement module for more information on the scales of measurement. This is an important first step because it will help you determine how best to organize the data. The data can typically be entered into a spreadsheet and organized or “coded” in some way that begins to give meaning to the data.
The next step would be to use descriptive statistics to summarize or “describe” the data. It can be difficult to identify patterns or visualize what the data is showing if you are just looking at raw data. Following is a list of commonly used descriptive statistics:
- Frequencies – a count of the number of times a particular score or value is found in the data set
- Percentages – used to express a set of scores or values as a percentage of the whole
- Mean – numerical average of the scores or values for a particular variable
- Median – the numerical midpoint of the scores or values that is at the center of the distribution of the scores
- Mode – the most common score or value for a particular variable
- Minimum and maximum values (range) – the highest and lowest values or scores for any variable
It is now apparent why determining the scale of measurement is important before beginning to utilize descriptive statistics. For example, nominal scales where data is coded, as in the case of gender, would not have a mean score. Therefore, you must first use the scale of measurement to determine what type of descriptive statistic may be appropriate. The results are then expressed as exact numbers and allow you to begin to give meaning to the data. For some studies, descriptive statistics may be sufficient if you do not need to generalize the results to a larger population. For example, if you are comparing the percentage of teenagers that smoke in private versus public high schools, descriptive statistics may be sufficient.
However, if you want to utilize the data to make inferences or predictions about the population, you will need to go anther step farther and use inferential statistics. Inferential statistics examine the differences and relationships between two or more samples of the population. These are more complex analyses and are looking for significant differences between variables and the sample groups of the population. Inferential statistics allow you test hypotheses and generalize results to population as whole. Following is a list of basic inferential statistical tests:
- Correlation – seeks to describe the nature of a relationship between two variables, such as strong, negative positive, weak, or statistically significant. If a correlation is found, it indicates a relationship or pattern, but keep in mind that it does not indicate or imply causation
- Analysis of Variance (ANOVA) – tries to determine whether or not the means of two sampled groups is statistically significant or due to random chance. For example, the test scores of two groups of students are examined and proven to be significantly different. The ANOVA will tell you if the difference is significant, but it does not speculate regarding “why”.
- Regression – used to determine whether one variable is a predictor of another variable. For example, a regression analysis may indicate to you whether or not participating in a test preparation program results in higher ACT scores for high school students. It is important to note that regression analyses are like correlations in that causation cannot be inferred from the analyses.
Finally, the type of data analysis will also depend on the number of variables in the study. Studies may be univariate, bivariate or multivariate in nature. The following Slideshare presentation, Quantitative Data Analysis explains the use of appropriate statistical analyses in relation to the number of variables being examined.
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