Common Mistakes

It may seem that there are many ways to make errors in working a statistics problem. In fact, most errors on statistics exams can be reduced to a short list of common oversights. If you learn to avoid the mistakes listed here, you can greatly reduce your chances of making an error on an exam.

  • Forgetting to convert between standard deviation (σ and s) and variance (σ2 and s2): Some formulas use one; some use the other. Square the standard deviation to get the variance, or take the positive square root of the variance to get the standard deviation.

  • Misstating one‐tailed and two‐tailed hypotheses: If the hypothesis predicts simply that one value will be higher than another, it requires a one‐tailed test. If, however, it predicts that two values will be different—that is, one value will be either higher or lower than another or that they will be equal—then use a two‐tailed test. Make sure your null and alternative hypotheses together cover all possibilities—greater than, less than, and equal to.

  • Failing to split the alpha level for two‐tailed tests: If the overall significance level for the test is 0.05, then you must look up the critical (tabled) value for a probability of 0.025. The alpha level is always split when computing confidence intervals.

  • Misreading the standard normal (z) table: All standard normal tables do not have the same format, and it is important to know what area of the curve (or probability) the table presents as corresponding to a given z‐score. Table 2 in "Statistics Tables" gives the area of the curve lying at or below z. The area to the right of z (or the probability of obtaining a value above z) is simply 1 minus the tabled probability.
  • Using n instead of n – 1 degrees of freedom in one‐sample t‐tests: Remember that you must subtract 1 from n in order to get the degrees‐of‐freedom parameter that you need in order to look up a value in the t‐table.
  • Confusing confidence level with confidence interval: The confidence level is the significance level of the test or the likelihood of obtaining a given result by chance. The confidence interval is a range of values between the lowest and highest values that the estimated parameter could take at a given confidence level.
  • Confusing interval width with margin of error: A confidence interval is always a point estimate plus or minus a margin of error. The interval width is double that margin of error. If, for example, a population parameter is estimated to be 46 percent plus or minus 4 percent, the interval width is 8 percent.

  • Confusing statistics with parameters: Parameters are characteristics of the population that you usually do not know; they are designated with Greek symbols (μ and σ). Statistics are characteristics of samples that you are usually able to compute. Although statistics correspond to parameters (equation is the mean of a sample, as μ is the mean of a population), the two are not interchangeable; hence, you need to be careful and know which variables are parameters and which are statistics. You compute statistics in order to estimate parameters.

  • Confusing the addition rule with the multiplication rule: When determining probability, the multiplication rule applies if all favorable outcomes must occur in a series of events. The addition rule applies when at least one success must occur in a series of events.

  • Forgetting that the addition rule applies to mutually exclusive outcomes: If outcomes can occur together, the probability of their joint occurrence must be subtracted from the total “addition‐rule” probability.

  • Forgetting to average the two middle values of an even‐numbered set when figuring median and (sometimes) quartiles: If an ordered series contains an even number of measures, the median is always the mean of the two middle measures.

  • Forgetting where to place the points of a frequency polygon: The points of a frequency polygon are always at the center of each of the class intervals, not at the ends.