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Unformatted text preview: The Chi-square ( χ 2 )Test Paul K. Strode, Ph.D., Fairview High School, Boulder, CO Consider the following scenario: A teacher had been teaching Pre-IB Biology for 10 years. Over those 10 years, he had kept track of the grade distributions in all of his classes—a total of 1,482 students. The teacher wondered if his observed grade distribution among his 1,482 students was rare when compared to what would be expected in a normal population of students. The data are summarized in Table 1. Table 1. Student grade distributions from 1999-2008 in Pre-IB Biology and the expected distributions for a normal population. 1999-2008 Expected Percent Distribution in a Normal Population Expected Distribution of Students in each Category out of 1,482 Grade Number of Students Percent A 415 28 10 148.2 B 504 34 20 296.4 C 356 24 40 592.8 D 148 10 20 296.4 F 59 4 10 148.2 Total 1,482 100 100 1,482 Can the teacher conclude that his observed student grade distribution is rare when compared to what would be expected in a normal population? In other words, is his distribution significantly different from a normal distribution, so much that it probably did not occur by chance? He can do a Chi-square Test on the data to determine the probability that his observed distribution occurred by chance. If the probability that his distribution occurred by chance is equal to or less than 0.05 (1/20), he can conclude that the differences between his observed distribution and what he would expect in a normal distribution are true differences and did not occur by chance alone . In other words, his students are truly a special population. Overview : Chi-square is a statistical test commonly used to compare observed raw data with data we would expect to obtain according to a specific hypothesis. For example the teacher above may hypothesize that the Pre-IB courses may attract students that in general are higher achieving than...
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This note was uploaded on 04/21/2011 for the course BIO 105 taught by Professor Staff during the Winter '08 term at Grand Valley State.
- Winter '08