Find the Patterns: Stats

To answer your strategic questions and gain a deeper understanding of your program’s impact, you will need to take your raw data and transform it using a combination of basic arithmetic and descriptive statistics to reveal patterns—both those that you expect to see and those that may be surprising.

Stats transform your data into high-level summaries of your variables, typically in a table or simple chart. These summaries will help you better visualize any patterns that may be present in your data. We will focus here on data collected to measure change in attitudes about service.

In this section we will discuss two types of stats: measures of central tendency and distribution.

  • Measures of central tendency

    By using measures of central tendency, you can look at the mean (average), median (middle data point) and mode (most frequently occurring data point) of your data. The first step is to create a table with all of your data, then use formulas to help calculate the mean, median and mode. Microsoft Excel can help you to do this.

    Example
    How much did this program change your opinion about the importance of service? Not at All A Little Somewhat Very Much
    1 2 3 4

    Pattern spotted: Overall, it looks like your program successfully influenced attitudes about service. On average, individuals who participated in the program said the program at least somewhat changed their opinion about the importance of service.

    Answer
    Mean 3.75
    Median 4.00
    Mode 4.00

    The mean is slightly lower than the median. Given that the median and mode are the same, this could mean there are a few low scores (outliers) pulling the mean down. The easiest way to look for outliers is to use a scatter plot, described in more detail in the distribution section below.

    Just because your data has outliers does not mean you need to discard anything, it simply provides a platform for asking more questions. Where did the outliers come from? Were there some individuals for whom the program did not change their opinion at all? Why did they feel that way?

    Learn more about central tendency.

  • Distribution

    Exploring distribution involves understanding how each of your data points relates to the data set as a whole. This can be done most easily with a chart or visualization. Visualizations that display your data points' distribution can be useful but also overwhelming. If you try a couple of charts and cannot make any sense of it, try summarizing your data into groups and then creating a visualization.

    Example
    How much did this program change your opinion about the importance of service? Not at All A Little Somewhat Very Much
    1 2 3 4

    Here is an example of a scatter plot. This gives you a sense that more people selected 3s and 4s, with a few outliers who selected 1, but you would have to count the dots individually to really find meaning in the data.



    When you organize the data in groupings like this, you can easily see that most individuals felt the program somewhat or very much changed their opinion about the importance of service.

    It may be more useful to look at your data by summarizing all of your data points into a table, grouping by question and response. You can organize this data into a table and also a bar chart.

    Number of Responses
    4 - Very Much 20
    3 26
    2 4
    1 - Not at All 2


  • Combining Central Tendency and Distribution

    Another way to explore central tendency and distribution is by creating a box plot (also called a box-and-whisker plot). A box plot combines measures of central tendency and distribution. It shows a summary of your data using mean, median and mode (central tendency) and how each of your data points relates to the data set as a whole using quartiles as the grouping (distribution).

    This is an example of a box plot for the post-program survey question outlined above. As you can see, the lower quartile (the bottom 25% of scores) begins at between 2 (“A little”) and 3 (“Somewhat”). This means that the rest of your respondents, 75% of individuals, recorded that the program affected their opinion about the importance of service.

    This type of chart is standard in Excel 2016 and available as a free add-on in other Excel packages.