Section 07 Generate descriptive statistics to explore your data
In addition to calculating the Indicator B8 percentage, you can explore your quantitative parent involvement data by generating descriptive statistics. Descriptive statistics provide information about the overall trends and distribution of the data. This includes reporting percentages or frequency distributions (also called “frequencies”) for nominal and ordinal data, as well as reporting summary statistics of interval and ratio data (see the section on coding quantitative data for more information about the different types of data). Click on the topics below to learn more.
Percentages
You may want to calculate the percentage of parents who provided responses to questions related to parent involvement beyond those questions directly related to Indicator B8. Remember, when sharing the percentages (internally or with stakeholders), be sure to also include the total number of people included in the calculation (e.g., the number of parents who responded to a certain category and the total number of parents who responded to the item). If you sampled, you may consider calculating the percentage of the sample that the respondents represent; otherwise, calculate the percentage of the total population that the respondents represent. Table 16 illustrates one way to do this for a fictional parent survey administered to a sample of 799 parents by State A.
| Item | Number of parents who responded to item | Item response rate | Number (and percent) of respondents who agree/ strongly agree/very strongly agree |
|---|---|---|---|
| The teacher communicates with me regularly about my child’s progress | 764 | 96% | 647 (85%) |
| My relationship with the school staff has a positive effect on my child’s education | 741 | 93% | 679 (92%) |
| Teachers are available to discuss my questions or concerns | 763 | 95% | 594 (78%) |
| The school explains what options I have if I disagree with the decision of the IEP team | 746 | 93% | 640 (86%) |
| I work together with the IEP team as an equal partner to develop my child’s IEP | 767 | 96% | 421 (55%) |
| IEP meetings are scheduled at times that are convenient to me | 784 | 98% | 323 (41%) |
As you examine the data presented in Table 16, there are a number of things that stand out:
- The item response rate is extremely high, which indicates that State A did a very good job designing its survey and making it clear to understand and easy for participants to respond to the questions
- Even though the item response rates were very high overall, they were lower for certain questions, which may indicate a reluctance to respond to those particular questions
- The percentage of parents who agreed somewhat (i.e., responded agree/strongly agree/very strongly agree) differed considerably based on the question.
Presenting additional information about the percentage of parents responding to items that go beyond Indicator B8 gives a fuller picture of the nature and extent of parent involvement in the state, including highlighting areas where improvements might be needed.
Reflect on the Data: Based on the results in Table 16, what changes could State A make to improve parent involvement in the state?
Frequencies
It can also be helpful to look at the frequency distribution of responses to survey items. The distribution is the range of values for an item. This provides a complete picture of the variation in responses to the item and can help you understand the data better. A simple way to create a distribution is to list every value (or response) of an item and the number of parents who provided each response, as shown in . Analysis software such as SPSS and SAS can easily generate tables like this one. You could also include information about the percentage of the total responses that each answer represents to give a better idea of where the responses fall.
Table 17
Frequency distribution of responses to the parent involvement survey in State A (Sample = 799)
Table 17
| Item | Very strongly disagree | Strongly disagree | Disagree | Agree | Strongly agree | Very strongly agree | # of parents who responded to item | Item response rate |
|---|---|---|---|---|---|---|---|---|
| The teacher communicates with me regularly about my child’s progress | 15 | 44 | 58 | 457 | 152 | 38 | 764 | 96% |
| My relationship with the school staff has a positive effect on my child’s education | 5 | 23 | 34 | 436 | 198 | 45 | 741 | 93% |
| Teachers are available to discuss my questions or concerns | 35 | 60 | 74 | 436 | 150 | 8 | 763 | 95% |
| The school explains what options I have if I disagree with the decision of the IEP team | 18 | 32 | 56 | 415 | 120 | 105 | 746 | 93% |
| I work together with the IEP team as an equal partner to develop my child’s IEP | 12 | 55 | 279 | 346 | 75 | 0 | 767 | 96% |
| IEP meetings are scheduled at times that are convenient to me | 72 | 155 | 234 | 232 | 91 | 0 | 784 | 98% |
Reflect on the Data: What do the results in tell you about how strongly parents responding to the survey feel about the efforts their school is making to facilitate parent involvement?
Summary statistics
Summary statistics are useful for providing additional descriptive information about your data. You can calculate summary statistics for interval or ratio data, and for ordinal data (if, as discussed in the section on coding quantitative data, you are treating ordinal survey responses as interval data for your quantitative analyses). It is easy to calculate summary statistics using software such as Microsoft Excel or statistical software such as SPSS, STATA, R, or SAS—as long as you have all of the survey responses entered into your data file correctly (see the section on creating a data file for more information).
Summary statistics you might consider include
- Minimum and maximum scores, to show where the responses fall (e.g., from 1-4 or 1-6)
- Measures of central tendency, which provide an idea of where the majority of scores are located in a distribution; these include
- Mean: the arithmetic average of a set of scores
- Median: the score above and below which 50 percent of scores fall
- Mode: the most frequently occurring score in the distribution
- Measures of variability, which indicate the spread of the scores in a distribution; three measures of variability include
- Range: the distance between the highest and lowest score in a distribution
- Variance: a measure of how far the scores in the distribution are spread out around the mean
- Standard deviation: the average distance of scores from the mean (the square root of the variance)
presents these summary statistics for the parent involvement survey administered by State A.
Table 18
Summary statistics for the State A parent involvement survey
Table 18
| Item | N | Minimum | Maximum | Mean | Median | Mode | Range | Variance | Std. Deviation |
|---|---|---|---|---|---|---|---|---|---|
| The teacher communicates with me regularly about my child’s progress | 764 | 1 | 6 | 4.05 | 4 | 4 | 5 | 0.880 | 0.938 |
| My relationship with the school staff has a positive effect on my child’s education | 741 | 1 | 6 | 4.26 | 4 |
4 |
5 | 0.674 | 0.821 |
| Teachers are available to discuss my questions or concerns | 763 | 1 | 6 | 3.83 | 4 | 4 | 5 | 1.034 | 1.017 |
| The school explains what options I have if I disagree with the decision of the IEP team | 746 | 1 | 6 | 4.21 | 4 | 4 | 5 | 1.145 | 1.070 |
| I work together with the IEP team as an equal partner to develop my child’s IEP | 767 | 1 | 5 | 3.54 | 4 | 4 | 4 | 0.682 | 0.826 |
| IEP meetings are scheduled at times that are convenient to me | 784 | 1 | 5 | 3.15 | 3 | 3 | 4 | 1.305 | 1.143 |
Reflect on the Data: What do the results in tell you about the variation in the way parents responded to the survey? What do the mean scores tell you? What about the variance and standard deviation? Do their responses tend to group together around the mean or are they spread out?
For some of the questions about parent involvement your state would like answered (e.g., To what extent do parents report satisfaction with their level of involvement in making decisions about their child’s education?), descriptive statistics such as percentages, frequencies and summary statistics may be sufficient to get the answers you need. However, for more complex questions—such as “Is there a statistically significant difference in the level of parent involvement in District A compared to the level of involvement in District B?”—you will likely need to conduct more advanced analyses, such as inferential statistical analyses, which we briefly discuss in the next section.