Yates' correction for continuity, or Yates' chi-square test, adjusts the formula for Pearson's chi-square test by subtracting 0.5 from the difference between each observed value and its expected value in a 2 × 2 contingency table. Continuity Correction Factor. This formula is chiefly used when at least one cell of the table has an expected count smaller than 5. In an experiment with 160 plants 50 of them were attacked. Origin of McNemar's Test: This test was formulated by Quinn McNemar in 1947. Let p be the proportion of plants of a certain kind that can be attacked by late blight. This addition of 1/2 to x is a continuity correction. It prevents overestimation of statistical significance for small data. Corrections for continuity: Most statistical textbooks at this point will note that critical values in their table (or any chi-square table for that matter) are approximate, but don’t say why. 2. This reduces the chi-square value obtained and thus increases its p-value. There is a problem with approximating the binomial with the normal. It’s called the “continuity correction”, or sometimes the Yates correction. Statistics: Continuity Correction When working with the normal distribution as an approximation to the binomial distribution, an adjustment, called a continuity correction, is made to the graph and calculations. Calculate the Z score using the Normal Approximation to the Binomial distribution given n = 10 and p = 0.4 with 3 successes with and without the Continuity Correction Factor The Normal Approximation to the Binomial Distribution Formula is below: True, Yes (default) False, No ← Click here to view the results. The continuity correction requires adding or subtracting .5 from the value or values of the discrete random variable X as needed. Hence to use the normal distribution to approximate the probability of obtaining exactly 4 heads (i.e., X = 4), we would ﬁnd the area under the normal curve from X = 3.5 to X = 4.5, the lower and upper boundaries of 4. 1. A continuity correction can also be applied when other discrete distributions supported on the integers are approximated by the normal distribution. That problem arises because the binomial distribution is a discrete distribution while the normal distribution is a continuous distribution. Identify that the solution will be a discrete whole number that will be shown on a normal distribution (which is always continuous). Corrections of this nature are common in both univariate settings, such as for inference on a single binomial proportion, and multivariate situations, such as contingency table analyses. Your text does explain the need to make a correction to the chi-square for low sample numbers. 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