Chi-Square Test free essay sample

Chi-square is a statistical test commonly used to compare observed data with data we would expect to obtain according to a specific hypothesis. For example, if, according to Mendels laws, you expected 10 of 20 offspring from a cross to be male and the actual observed number was 8 males, then you might want to know about the goodness to fit between the observed and expected. Were the deviations (differences between observed and expected) the result of chance, or were they due to other factors.How much deviation can occur before you, the investigator, must conclude that something other than chance is at work, causing the observed to differ from the expected. The chi-square test is always testing what scientists call the null hypothesis, which states that there is no significant difference between the expected and observed result. The formula for calculating chi-square ( ) is: 2= (o-e) ? /e That is, chi-square is the sum of the squared difference between observed (o) and the expected ( e) data (or the deviation, d), divided by the expected data in all possible categories. We will write a custom essay sample on Chi-Square Test or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page Determine a relative standard to serve as the basis for accepting or rejecting the hypothesis. The relative standard commonly used in biological research is p ; 0. 05. The p value is the probability that the deviation of the observed from that expected is due to chance alone (no other forces acting). In this case, using p ; 0. 05, you would expect any deviation to be due to chance alone 5% of the time or less. . Refer to a chi-square distribution table Using the appropriate degrees of freedom, locate the value closest to your calculated chi-square in the table. Determine the closest probability(p) value associated with your chi-square and degrees of freedom. Step-by-Step Procedure for Testing Your Hypothesis and Calculating Chi-Square 1. State the hypothesis being tested and the predicted results. Gather the data by conducting the proper experiment (or, if working genetics problems, use the data provided in the problem). 2.Another way of looking at that is to ask if the frequency distribution fits a specific pattern. Two values are involved, an observed value, which is the frequency of a category from a sample, and the expected frequency, which is calculated based upon the claimed distribution. The derivation of the formula is very similar to that of the variance which was done earlier (chapter 2 or 3). The idea is that if the observed frequency is really close to the claimed (expected) frequency, then the square of the deviations will be small.The square of the deviation is divided by the expected frequency to weight frequencies. A difference of 10 may be very significant if 12 was the expected frequency, but a difference of 10 isnt very significant at all if the expected frequency was 1200. If the sum of these weighted squared deviations is small, the observed frequencies are close to the expected frequencies and there would be no reason to reject the claim that it came from that distribution. Only when the sum is large is the a reason to question the distribution. Therefore, the chi-square goodness-of-fit test is always a right tail test.