EZReport calculations

Single-choice

When EZReport scans the database, it computes the number of records (as selected by a query) which belong to each category. For single-choice question, categories are designated by short codes, and matching records have a single short code in the appropriate field. A record is counted as a miscode if it is ambiguous or does not match any of the available response codes.

Response code	Data value	Match?
A	A	Yes
Seattle	Seattle	Yes
A	a	No
A	A,b	No

Combo box

Combo box questions are similar to single choices, except that code values are not sensitive to case, since they may be typed in by the respondent as well as selected from a list

Response code	Data value	Match?
A	A	Yes
A	a	Yes

Summary statistics

Only data values that evaluate to a well-formed number are used in calculating summary statistics. Leading and trailing whitespace are ignored.

Data value	Number value
5	5.0
	Error
-0.0	0.0
ten	Error
-8.5e4	-85000.0
5,8	Error
4 inches	Error

The Average, Standard Deviation, and Standard Error calculations neglect records whose data values do not properly evaluate to numbers. All calculations are performed with 64-bit floating-point numbers. Rounding is done by the CPU.

Plots

Bar and pie plots are scaled according to the number of responses matching each category. Percentages are then calculated based on the number of records represented in the plot. Here are four plots of the same data set. The numbers of responses are the same, but the percentages differ, depending on which columns are shown.

Standard set of responses
with X (Don't know)
with Blank (unanswered) records
with Miscodes (unrecognized responses)

Statistics

In accordance with social science conventions, the median is presented as a decimal value. For the above data, the responses can be sorted like this, where the median falls in the middle. Since the center of the table (black line) falls 2/3 of the way to the top of the "3" block, the median is declared to be 2.67.

1

2

2

2

2

3

3

3

3

3

3

3

3

3

4

4

4

4

5

5

6

6

If all the responses were "6" in this example, the median should be 6, indicating a high score. If all the responses were "1", the median would have to be 1. If there were two responses, "1" and "2", the median would be 1.5.

Non-numeric codes like X, blanks, and miscodes are disregarded for the median, average, and standard deviation calculations. The Standard Error line means "Standard error of the mean," simply (Standard deviation/ (sqrt(Total))).

Percentages

Since this is a single-choice question, the sum of the percentages should add up to 100%. However, rounding can cause a slight deviation from 100%.

One decimal. Total  = 99.8%
Two decimals. Total = 100.01% We might think that the preceding graph should have printed 4.4% instead of 4.3% ...
Three decimals. Total = 100.000% ... but 1/23 does not have a convenient decimal representation. 1/23 = 0.04347826086...

Multiple-response questions are often confusing. The percentages in these plots mean "The fraction of respondents who answered X." Since each person can make more than one answer, the sum of the percentages will usually exceed 100%. A crosstab table of the question shows why that occurs with this interpretation of percentage. The other interpretation of percentage would be "The fraction of all responses represented by this block," which is not usually what analysts want when they make reports.

Bar plot
Crosstab table