 is still possible for the sample’s responses to be different than that of the whole population. Responsible pollsters and survey researchers never report a point estimate alone. Rather, they report xx things: the point estimate, a confidence interval around the point estimate that gives the highest and lowest value the actual population response could have, a confidence level stating how certain they are that the real population response is within the range of percentages covered by the confidence interval, and the size of (number of respondents in) the sample. 95% is the lowest confidence level commonly used; some researchers are more demanding and want to be 99% sure but this means having to widen the confidence interval. Sample size needs to be more than 100 for the confidence interval calculations to be correct; most pollsters prefer larger samples than that, particularly on national questions.
Calculating the confidence interval for 95% uses the formula that applies to proportions since polls are expressed in % of respondents answering a particular way. This formula is:
c.i. = Proportion of the sample + 1.96 multiplied by the square root of (.5 x .5) divided by the sample size. 1.96 is a constant that generated the interval matching a 95% confidence level and .5 is a constant used to make sure the interval is set at its maximum extent. (Those who want the explanation of why this works can consult Joseph F. Healey, Statistics for Social Research, 6th edition (2002), pp. 173-174 and background on pp. 165-168.)
Now you can see how an election can be “too close to call.” If pollsters survey their random samples of likely voters and 48% say they will vote for Arnold and 52% say they will vote for Condi but calculate that their sampling error is 3%, the pollsters have to acknowledge that Arnold could get anywhere from 45 to 51% of the vote and Condi anywhere from 49 to 55%. Condi looks like she has a lead, but with an overlap in confidence intervals, pollsters will report results but not predict a winner. They will leave picking winners to the bettors in Las Vegas and elsewhere.
© 2006, M.J. Peterson. This is the course website for PoliSci 399, Department of Political Science. University of Massachusetts Amherst. Produced and maintained by M.J. Peterson, email@example.com.