The 30th Annual Phi Delta Kappa/Gallup Poll of the Public's Attitudes Toward the Public Schools |
SAMPLING TOLERANCES
In interpreting survey results, it should be borne in mind that all sample surveys are subject to sampling error, i.e., the extent to which the results may differ from what would be obtained if the whole population surveyed had been interviewed. The size of such sampling error depends largely on the number of interviews.
The following tables may be used in estimating the sampling error of any percentage in this report. The computed allowances have taken into account the effect of the sample design upon sampling error. They may be interpreted as indicating the range (plus or minus the figure shown) within which the results of repeated samplings in the same time period could be expected to vary 95% of the time, assuming the same sampling procedure, the same interviewers, and the same questionnaire.
The first table shows how much allowance should be made for the sampling error of a percentage:
Recommended Allowance for Sampling Error of a Percentage | |||||||
In Percentage Points | |||||||
1,500 |
1,000 |
750 |
600 |
400 |
200 |
100 | |
| Percentages near 10 | 2 |
2 |
3 |
3 |
4 |
5 |
8 |
| Percentages near 20 | 3 |
3 |
4 |
4 |
5 |
7 |
10 |
| Percentages near 30 | 3 |
4 |
4 |
5 |
6 |
8 |
12 |
| Percentages near 40 | 3 |
4 |
5 |
5 |
6 |
9 |
12 |
| Percentages near 50 | 3 |
4 |
5 |
5 |
6 |
9 |
13 |
| Percentages near 60 | 3 |
4 |
5 |
5 |
6 |
9 |
12 |
| Percentages near 70 | 3 |
4 |
4 |
5 |
6 |
8 |
12 |
| Percentages near 80 | 3 |
3 |
4 |
4 |
5 |
7 |
10 |
| Percentages near 90 | 2 |
2 |
3 |
3 |
4 |
5 |
8 |
| *The chances are 95 in 100 that the sampling error is not larger than the figures shown. | |||||||
The table would be used in the following manner: Let us say that a reported percentage is 33 for a group that includes 1,000 respondents. We go to the row for ''percentages near 30'' in the table and across to the column headed ''1,000.''
The number at this point is 4, which means that the 33% obtained in the sample is subject to a sampling error of plus or minus four points. In other words, it is very probable (95 chances out of 100) that the true figure would be somewhere between 29% and 37%, with the most likely figure the 33% obtained.
In comparing survey results in two samples, such as, for example, men and women, the question arises as to how large a difference between them must be before one can be reasonably sure that it reflects a real difference. In the tables below, the number of points that must be allowed for in such comparisons is indicated. Two tables are provided. One is for percentages near 20 or 80; the other, for percentages near 50. For percentages in between, the error to be allowed for lies between those shown in the two tables.
Recommended Allowance for Sampling Error of the Difference | ||||||
TABLE A |
In Percentage Points | |||||
Size of Sample |
1,500 |
1,000 |
750 |
600 |
400 |
200 |
1,500 |
4 |
|||||
1,000 |
4 |
5 |
||||
750 |
5 |
5 |
5 |
|||
600 |
5 |
5 |
6 |
6 |
||
400 |
6 |
6 |
6 |
7 |
7 |
|
200 |
8 |
8 |
8 |
8 |
9 |
10 |
TABLE B |
Percentages near 50 | |||||
Size of Sample |
1,500 |
1,000 |
750 |
600 |
400 |
200 |
1,500 |
5 |
|||||
1,000 |
5 |
6 |
||||
750 |
6 |
6 |
7 |
|||
600 |
6 |
7 |
7 |
7 |
||
400 |
7 |
8 |
8 |
8 |
9 |
|
200 |
10 |
10 |
10 |
10 |
11 |
13 |
| *The chances are 95 in 100 that the sampling error is not larger than the figures shown. | ||||||
Here is an example of how the tables would be used: Let us say that 50% of men respond a certain way and 40% of women respond that way also, for a difference of 10 percentage points between them. Can we say with any assurance that the 10-point difference reflects a real difference between men and women on the question? Let us consider a sample that contains approximately 750 men and 750 women.
Since the percentages are near 50, we consult Table B, and, since the two samples are about 750 persons each, we look for the number in the column headed ''750,'' which is also in the row designated ''750.'' We find the number 7 here. This means that the allowance for error should be seven points and that, in concluding that the percentage among men is somewhere between three and 17 points higher than the percentage among women, we should be wrong only about 5% of the time. In other words, we can conclude with considerable confidence that a difference exists in the direction observed and that it amounts to at least three percentage points.
If, in another case, men's responses amount to 22%, say, and women's to 24%, we consult Table A, because these percentages are near 20. We look in the column headed ''750'' and see that the number is 5. Obviously, then, the two-point difference is inconclusive.
TOPICS:
Introduction to the Poll
Public Versus Nonpublic Schools
Grading the Schools
Effectiveness of Public Schools
Improving the Nation's Inner-City Schools
Politics and the Public Schools
Problems Facing the Public Schools
School Operation/Curriculum
Impact of Unions
The Public's Knowledge of Local Schools
Confidence in Institutions
Closing Comments
How to Order the Poll
Research Procedure
Sampling Tolerances
Design and Composition of the Sample
Conducting Your Own Poll
PDK Home
| Site Map
|
