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STATS TO DETERMINE WHAT IS NORMAL!! 2 TYPES OF STATS DESCRIPTIVE – SUMMARIZES A SET OF DATA INFERENTIAL – INTERPRET DATA AND DRAW CONCLUSIONS (What can we infer about the population from data gathered by the sample?) Example EXAMPLE – In a recent study volunteers who had less than 6 hours of sleep were 4 times more likely to answer incorrectly on a science test than were participants who had at least 8 hours of sleep. Which part is descriptive? Inferential? Graphs TO GET A BETTER SENSE OF DATA, INFORMATION CAN BE PUT ON HISTOGRAMS – BAR GRAPHS OR FREQUENCY POLYGONS – LINE GRAPHS MEASURES OF CENTRAL TENDENCY MEAN MEDIAN MODE REPRESENT WAYS TO SUMMARIZE DESCRIPTIVE STATISTICS Misleading Suppose your Mom wants you to attend a family reunion on Sunday Everyone in the family protests Your Mother attempts to separately convince each family member that it will not be so bad Mom Mom tells your younger sister that the average age is 10 She tells you the average age is 18 She tells your Dad it is 36 Everyone feels better about going Did Mom lie? Attendees Attendees’ ages 3, 7, 10, 10, 15, 17, 18, 44, 49, 58, 59, 82, 96 What is the mean, median, mode? Did Mom lie? NORMAL DISTRIBUTION BELL SHAPED CURVE POSITIVELY AND NEGATIVELY SKEWED – DIRECTION OF THE TAIL The tail tells the tale!!! EXAMPLE – POSITIVELY – ALL STUDENTS FAIL A QUIZ AND 2 MAKE 100’S NEGATIVELY – ALL STUDENTS MAKE “A’s” ON A QUIZ AND 1 FAILS MEASURES OF VARIABILITY DESCRIBES THE SPREAD OF SCORES INCLUDES: RANGE, STANDARD DEVIATION, AND VARIANCE (SD squared) RANGE – LOWEST SCORE SUBTRACTED FROM THE HIGHEST SD – SQUARE ROOT OF THE VARIANCE Variability If you collected the ages of all students in the 11th grade there would be little variability. If you collected the shoe sizes of all students in the 11th grade there would be greater variability. One outlier can greatly affect the range. SCORES Z SCORES – THE MEAN SCORE OF A DISTRIBUTION HAS A Z SCORE OR STANDARD SCORE OF ZERO. 1 STANDARD DEVIATION ABOVE THE MEAN HAS A Z SCORE OF 1. ANOTHER TYPE OF SCORES ARE PERCENTILE SCORES – AT OR BELOW A PARTICULAR SCORE CORRELATION RELATIONSHIP BETWEEN 2 VARIABLES CAN BE POSITIVE – ONE VARIABLE INCREASES AND THE OTHER INCREASES NEGATIVE – ONE VARIABLE INCREASES AND ONE DECREASES NONE - ZERO Examples How is studying related to grades? How is playing video games related to grades? SCATTERPLOTS ILLUSTRATE THE STRENGTH AND DIRECTION OF CORRELATIONS CORRELATION COEFFICIENT VARIES FROM -1 TO +1. STRENGTH OF RELATIONSHIP IS SHOWN BY THE COEFFICIENT. CLOSER TO -1 OR +1 – THE STRONGER THE RELATIONSHIP A NONE OR ZERO CORRELATION HAS NO RELATIONSHIP INFERENTIAL STATS CAN WE GENERALIZE FROM A CHOSEN SAMPLE TO THE LARGER POPULATION? P – VALUE – INDICATES STATISTICAL SIGNIFICANCE LESS THAN 1 IN 20 PROBABLITY OF BEING CAUSED BY CHANCE .05 Lower the p value - the more significant