Chapter 6: Misconceptions When people read, hear, or prepare research summaries, they sometimes have misconceptions about what is or isn't "sound practice" regarding the collection, analysis, and interpretation of data. Here are some of these common (and dangerous) misconceptions associated with the content of Chapter 6. A random sample will be exactly like the population, just smaller. Doubling the size of the sample cuts the standard error in half. To estimate the standard error, many samples must be extracted from the population. If the sample size is increased, the height of the sampling distribution's "modal" point will move even further away from the baseline. If a newspaper claims, after polling a sample of voters during a political race, that Candidate X is ahead of Candidate Y by 15 percentage points "with a margin of error of ±3," then Candidate X is ahead of Candidate Y by between 12 and 18 percentage points at the time the poll was taken. If a population became larger, it would be necessary to increase the size of the sample in order to maintain the same standard error. Once a confidence interval is set up, the parameter will lie somewhere between the CI's upper and lower end-points. The end-points of a confidence interval are always equidistant from the sample statistic. If a researcher reports M±SEM, that's equivalent to a 68% CI built around the mean. If a fair coin is repeatedly flipped and examined to see how it hands, and if there are 56 heads and 44 tails after 100 flips, it's likely that the number of heads after 200 flips will be smaller than 106.