Quantitative Analysis
The next step is to analyze the data. The most frequently used calculations for analyzing quantitative data from program evaluations are averages, weighted averages, percentages, and frequency distributions (all described below). For most evaluations, these types of calculations are adequate for understanding the results.
An Excel spreadsheet can be used to tally responses and simple formulas can be inserted to calculate averages and percentages. There are also many statistical software packages like SAS, STATA and SPSS that can do high-level statistical analyses but advanced computer and statistics skills are needed to use them.
Averages
An average is a calculation of the typical value of all items in a set of data. It does not necessarily represent the middle value or the most commonly occurring value, but rather gives an overall picture of the common value. For example, if a survey asks the respondent's age, the data can be used to calculate the average age of all respondents by adding up everyone's ages and dividing by the number of people.
Formula: sum of all responses / total number of responses = the average
Example:
If 8 people complete a survey questionnaire and respond that their ages are 32, 43, 35, 38, 29, 44, 36 and 39, the sum of their ages would be 296.
296 / 8 people = an average age of 37
Weighted averages
Weighted averages allow you to compare responses to a set of items that have the same response options. This is typically used when you have a rating question and want to compare the average "score" for more than one option. The calculation involves assigning a value (or weight) to each response option in the rating scale—which usually rating questions will already have—and calculating an average score for each item that you'd like to compare. This means that some responses assigned a higher "weight" will contribute more to the final average than lower "weight" responses.
Example:
Say a questionnaire asks respondents to rate how often they adhere to various health-related behaviors. The following table shows how many out of the 50 respondents chose each answer for two of the questions: "Eat a healthy diet" and "Exercise." Notice that one person did not respond to the question on diet, so there are a total of only 49 responses.
| Healthy behaviors | Almost never (value=1) | Some of the time (value=2) | Most of the time (value=3) | All the time (value=4) | No response |
|---|---|---|---|---|---|
| Eat a healthy diet | 4 | 14 | 30 | 1 | 1 |
| Exercise | 21 | 18 | 9 | 2 | 0 |
To calculate a weighted average for the "Eat a healthy diet" item (see table below):
- Multiply the response option's assigned value (or weight) by the number of times the response option was selected.
- Add the total (weight x number of responses) for all options.
- Divide that total by the total number of responses.
"How often do you eat a healthy diet?"
| Response option |
Weight | # responses | Weight x # responses |
|---|---|---|---|
| Almost never | 1 | 4 | 4 |
| Some of the time | 2 | 14 | 28 |
| Most of the time | 3 | 30 | 90 |
| All the time | 4 | 1 | 4 |
| Total | 49 | 126 | |
126 / 49 respondents = 2.6 weighted average score for "Eat a healthy diet."
This weighted average score can then be used to compare reported levels of "Eat a healthy diet" to other items with the same response options (e.g., "Check blood glucose levels," "Exercise," "Take medications"). For example, the weighted average for "Exercise" is calculated in the same way.
"How often do you exercise?"
| Response option |
Weight | # responses | Weight x # responses |
|---|---|---|---|
| Almost never | 1 | 21 | 21 |
| Some of the time | 2 | 18 | 36 |
| Most of the time | 3 | 9 | 27 |
| All the time | 4 | 2 | 8 |
| Total | 50 | 92 | |
92/ 50 = 1.8 weighted average score for "Exercise."
These calculations allow us to better see the relationship between the two items. We can say that, on a scale of 1-4 (with 4 being all of the time), the weighted average score for "Exercise" (1.8) is lower than that for "Eat a healthy diet" (2.6). When reporting results for a rating question, using a weighted average allows you to report a single number, which may make it easier for your audience to understand the results. (The alternative would be to report frequency and/or percentage of number of respondents for each response option, which might be too much information for a given audience.) In the example above, respondents are less likely to report that they exercise regularly than that they eat a healthy diet. If this was a key piece of your evaluation, it could inform future programming that might focus more on exercise than on healthy eating.
Percentages
Percentages allow you to show relationships and make comparisons, such as what proportion of respondents selected each of the given responses to a question.
A table showing the number of items falling within each response category is known as a frequency distribution. A frequency distribution often includes not only the number of times, or frequency, with which an item appears, but also the proportion of respondents chose each response option for a question.
Example:
Here we can see a sample survey question about participation in a diabetes prevention program, followed by the resulting frequency distribution for the responses.
How many months have you been participating in the diabetes prevention program?
Less than 1 month
1–3 months
4–6 months
7–9 months
10–12 months
The following table shows the frequency distribution of responses to this question. Note that, of the 50 people who returned the questionnaire, 2 did not respond to this question. Therefore, percentages for the response options were calculated using 48 (total number of responses) as the denominator.
For example, 7 / 48 = 15% of respondents who chose "Less than one month" as their response. Each of the other percentages is calculated similarly.
| Response option | # responses | %* |
|---|---|---|
| Less than 1 month | 7 | 15 |
| 1–3 months | 12 | 25 |
| 4–6 months | 22 | 46 |
| 7–9 months | 5 | 10 |
| 10–12 months | 2 | 4 |
| Total | 48 | |
| No response | 2 |
*rounded to the nearest percent
Reporting
Put the results of your analysis in a format that is clear and understandable. Quantitative data can be synthesized and visually displayed in tables, graphs, charts, or maps. Displaying the results visually often makes them easier to review and interpret.
ERC Worksheet 6: Data Analysis and Interpretation
EXERCISE : Once you have determined which data collections methods you will use and have developed protocols for collecting the information, you want to think about how you will organize, analyze, and interpret the data. For each of your data collection protocols/instruments, complete ERC Worksheet 6, which will help you stick to asking only the most important, useful types of questions.
Click on the PDF documents in the sidebar to see examples of how this step was completed for our case study sites.
Northwest Center for Public Health Practice (2011). Data collection for program evaluation.
Data Analysis
ERC Worksheet 6 
Analyze the Data and Synthesize Results
