range and averages
Some terms that might be new to readers:
- Correlation Coefficient – Correlations measure the strength and direction of a linear relationship between the two variables. The correlation between any variable and itself is always 1. The correlation between two variables can be positive, indicating that as one score increases, so does the other or vice versa. The correlation coefficient can range from -1 to +1, with -1 indicating a perfect negative correlation, +1 indicating a perfect positive correlation, and 0 indicating no correlation at all.
- Example – You can think of the correlation coefficient as telling you the extent to which you can guess the value of one variable given a value of the other variable. Say that I had a correlation of +0.5 between participants and edit count. That would mean that in a mojority of cases, an increase in participants is associated with an increase in edit count.
- Interquartile Range – Also known as the middle 50, where a distribution is ordered and grouped into quartiles, the interquartile range is the range of values between the first and the fourth quartiles.
- Example – Imagine that you have a distribution of 3, 5, 6, 7, 7, 7, 8, 9, 10, 10, 11, 12, you order the values and split them into four quartiles of data, for this example, 3 numbers each: Quartile 1= From 3 to 6, Quartile 2 from 7 to 7, Quartile 3 from 8 to 10, and Quartile 4 from 10 to 12; surrounding a median of 7.5 (7.5 as the mean of the two middle numbers 7 and and 8, since number of distribution values is even). The interquartile range is then 7 to 10. Here, we have a more narrow, "average," range of response, those falling around the median to get a better picture of average without the confusion of high or low performing outliers in the distribution.
- Mean- This is the number that is most representative or typical of the group. You discover this by adding all the numbers up and dividing the total by how many numbers you added up.
- Example – A program leader reports on six photo upload competitions that happened over a year. They report the number of participants at these six events: 10, 6, 15, 7, 10 and 8. To find the average, you add those numbers up to get 56. You then divide 56 by 6 (the number of events reported on) to get an average of: 9.3.
- Median – The median is the middle number in a group of numbers.
- Example – For the set of numbers that is: 3, 5, 6, 7, 7, 7, 8, 9, 10, 10, the median is 7
- Mode – The mode is the most commonly seen number in a group of numbers.
- Example – For the set of numbers that is: 3, 5, 6, 7, 7, 7, 8, 9, 10, 10, the mode is 7
- Range – This is the difference between the lowest and highest numbers reported. You find a range by subtracting the lowest number from the highest number reported.
- Example – Five editathons have reported user retention numbers of: 3, 6, 7, 9, 12. To find the range, subtract 3 from 12, which equals 9. 9 is the range.
- Standard deviation (SD) – This is the measurement of how spread out numbers are from the mean. Read the Wikipedia article about standard deviation. The smaller the standard deviation, the smaller the range of responses in a distribution, and vice-versa. Importantly, when the value of the standard deviation exceeds the mean value, the range is extreme and the mean is an unreliable measure of average.
- How are they used in this report?
In this report, the range might seem like an obvious measure of distribution of the numbers reported. However, the average in a group of numbers is not as evident. Most of the time, averages are represented as means, medians or modes.
Often in reporting, you may only see means reported or depicted. Usually reports of mean scores are accompanied by report of the standard deviation which indicates the distribution of values, assuming a normal distribution. Although means and standard deviations are also shared in this report, the data do not meet the assumptions of normality and mean scores are not the best measure of «averages» in most cases.
For this reason, averages reported in the current reports refer to the median response. While the means and standard deviations (SD) are reported in the notes references that follow each reported median, they are there for the purpose of triangulation of averages and demonstration of the often extreme range and variability in reported values. Means and standard deviations have also been rounded as they are, for the most part, not a precise measure of average, and specificity down to the tenth is not pertinent. Modes would also be reported, however, in nearly all cases there were no valid mode values due to the range of response values exceeding the number of responses. Where there are valid modes, they are reported.
The report uses a variety of graphs to depict data:
- Bar graphs
- Bar graphs show the extent to which a metric value is observed, or reported, within a set of data. Bar graphs allow for easy comparison of a metric over time or across groups and other categories.
Here's an example of a pie chart
. This one shows the average length of an editathon, as reported in 2013.
- Pie charts
- Pie charts show the size of responses using the numerical response to determine how big the «slices» of the pie are.
- Scatter plots
- Scatter plots are charts that graph the points of intersection of two variables, or points of data reported.
- To do this, each variable is associated differently around a grid of possible responses; one variable is measured along the x-axis and the other along the y-axes.
- Within the scatter plot area, each variable intersection reported in a set of data (one intersection for each individual report of data) is plotted as a separate point on the graph to illustrate where the two variables intersect, or meet, for all the pairing of those variables.
- Bubble chart
- Bubble charts are more advanced than a scatter plots. Bubble graphs plot data in 3D by using bubble size in order to graph three-dimensions, or variables/data points.
- Just like scatter plots, bubble graphs use the x- and y-axes to show the intersection of two different variables for all the pairings of those variables that were reported.
- Additionally, the 3D bubble graph uses different sized "bubbles" to show the intersection of values of a third variable along the three-dimensional z-axis.
- In this report, the bubbles are labeled with the variable that is represented by their bubble size, and the x- and y- axis will have their own values noted on their appropriate scales.
- Tip – Make sure to always read the axis labels and bubble size legend included with each chart.
- Box plot
- A box plot is a way of depicting groups of numeric data using their quartiles.
- The vertical lines running below and above the box plot area (also called tails or whiskers) depict the full range of values reported for a variable while the shaded box area illustrates the 25% of values reported that fall below the median (Quartile 2), and the 25% of values reported that fall above the median value (Quartile 3) reported.
- That is, the area contained within the box of the box plot depicts the interquartile range and includes the middle 50% of all reported values, the ones that fall closest to the «average».
- The length of the vertical distribution line beyond the box itself illustrates the full range of responses. Here, we look at the average range of most responses, those falling around the median, to get a better picture of average without the confusion of high or low performing outliers that exist within the distribution.