Calculators±0.49 percentage points. For example, with a reported margin of error of ±4%, the lower and upper limits will be calculated using 4.49 and 3.51, respectively. (Recall that margin of error is inversely related to sample size.)
Estimated Population Percentage and Margin of Error
Estimating Sample Size when the Report of a Poll Fails to Provide that Essential Bit of Information
Significance of the Difference between the Results of Two Separate Polls
Significance of the Difference between the Results for Candidate X and Candidate Y in a Single Poll
Calculator 1: Estimated Population Percentage and Margin of Error
This calculator can be used for analyzing the results of a poll of your own (in which case, keep in mind the requirement of a representative sample) or for checking the preciseness of the results of polls reported in the news media. Enter the respective percentages of respondents within the sample who favor Candidate X and Candidate Y into the top two cells; enter the size of the sample into the third cell; and then click the "Calculate" button. This calculator will also work if the sample percentage for only one of the candidates is entered.
Note: For polls reported in the news media, the margins of error tend to be rounded to the nearest integer. They also often appear to be based on the percentage for the candidate who has the majority or plurality within the sample.
Calculator 2: Estimating Sample Size when the Report of a Poll Fails to Provide that Essential Bit of Information
It occasionally happens that the press report of a poll will give no indication of the size of the sample on which the poll is based. In cases if this sort, Calculator 2 will estimate the size of the sample on the basis of two items of information that probably will be given in the report: the margin of error and the largest of the candidate percentages. If the reported margin of error is entered as an integer, the programming for Calculator 2 will assume it to be a rounded value and calculate the lower and upper limits of estimated sample size based on the reported margin of error
|XI ||The percentage reported for Candidate X in poll I||nI ||The size of poll I||XII ||The percentage reported for Candidate X in poll II||nII ||The size of poll II|
|Poll I||Poll II
Mere-chance probability of |
the observed difference
|1.||the split (e.g., 52/48, 46/54) between the reported percentages for the two major candidates, X and Y, and||2.||the 50/50 split that would be expected if there were no difference between the percentages of preference for the candidates within the general population.|
"significance of the difference"T
All tests of statistical significance involve a comparison between
The bottom line in such a test is a probability value, ranging between 0.0 and 1.0, which represents the likelihood that a difference between (1) and (2) as great as the one observed might have occurred through mere chance. By the conventional canons of statistical inference, a probability value equal to or less than 0.05 is regarded as
an observed result; and
the result one would expect to find, on average, if nothing other than mere chance coincidence, mere random variability, were operating in the situation.
while any value larger than 0.05 is regarded as
significant == fairly unlikely to have occurred through mere chance,
non-significant == fairly likely to have occurred through mere chance.
Multiplying a probability value by 100 converts it into a more intuitively accessible percentage measure. Thus, a probability of 0.049 represents a 4.9% chance that the observed difference might have occurred through mere random variability; a probability of 0.1152 represents an 11.52% chance; and so forth.
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