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Chapter 14 Quantitative Analysis: Descriptive Statistics - Coggle Diagram

- - - - Data entry. Coded data can be entered into a spreadsheet, database, text file, or directly into a statistical program like SPSS. Most statistical programs provide a data editor for entering data.
        
        Missing values. Missing data is an inevitable part of any empirical data set. Respondents may not answer certain questions if they are ambiguously worded or too sensitive. Such problems should be detected earlier during pretests and corrected before the main data collection process begins.
        
        Data transformation. Sometimes, it is necessary to transform data values before they can be meaningfully interpreted. For instance, reverse coded items, where items convey the opposite meaning of that of their underlying construct, should be reversed (e.g., in a 1-7 interval scale, 8 minus the observed value will reverse the value) before they can be compared or combined with items that are not reverse coded.
- - - - Dispersion refers to the way values are spread around the central tendency, for example, how tightly or how widely are the values clustered around the mean. Two common measures of dispersion are the range and standard deviation.
        
        The range is the difference between the highest and lowest values in a distribution.
        
        Standard deviation, the second measure of dispersion, corrects for such outliers by using a formula that takes into account how close or how far each value from the distribution mean:
        
        The square of the standard deviation is called the variance of a distribution. In a normally distributed frequency distribution, it is seen that 68% of the observations lie within one standard deviation of the mean (µ + 1 σ), 95% of the observations lie within two standard deviations (µ + 2 σ), and 99.7% of the observations lie within three standard deviations
      - Lastly, the mode is the most frequently occurring value in a distribution of values. In the previous example, the most frequently occurring value is 15, which is the mode of the above set of test scores.
      - Note that any value that is estimated from a sample, such as mean, median, mode, or any of the later estimates are called a statistic.
      - The second measure of central tendency, the median, is the middle value within a range of values in a distribution. This is computed by sorting all values in a distribution in increasing order and selecting the middle value.
      - The arithmetic mean (often simply called the “mean”) is the simple average of all values in a given distribution