CHAP 17 CHI (Kahy) SQURE 1 PARAMETRIC AND NONPARAMETRIC STATISTICAL TESTS PARAMETRIC tests are more accurate than NONPARAMETRIC tests because they have 3 assumptions (research). 1. Random selection 2. Independent of observation 3. Sample is taken from a normal population with a normal distribution 2 3 NONPARAMETRIC STATISTICAL TESTS CHI SQURE is like frequency distribution (Chap 2) It is used for comparative studies. Ex1. Of the two leading brands of cola, which is preferred by most Americans? 4 CHI SQURE Ex2. which psychotherapy technique is used by most psychologists? i.e. cognitive, behavioral, humanistic, CBT, psychodynamics, etc. 5 CHI SQURE = Σ(fo-fe)² /fe fo= observed frequency fe= expected frequency df = C-1 C= number of categories fe = n/c = Ho n= sample size 6 CHI SQURE 7 df=C-1 8 9 Problems Distribution of Eye colors for a sample of n=40 individuals. FYI From chapter 2 Frequency Distribution (X )eye colors (f ) frequencies Blue 12 Brown 21 Green 3 Other 4 see next slide for Chi square 10 Problems Distribution of Eye colors for a sample of n=40 individuals. Frequency distribution Fo Blue Brown Green Others 12 21 3 4 11 The question for the hypothesis test is whether there are any distribution of the four possible eye colors. Are any of the eye color distribution would be expected simply by chance? We will set alpha at α =.05 Step 1) H0 : fo = fe no preference for any specific eye color H1 : fo ≠ fe preference for specific eye color 12 Problems Distribution of Eye colors for a sample of n=40 individuals. Frequency distribution Blue fo fe Brown Green Others 12 21 3 4 10 10 10 10 13 Step 2 df=C-1 14 Problems A psychologist examining art appreciation selected an abstract painting that had no obvious top or bottom. Hangers were placed on the painting so that it could be hung with any one of the four sides at the top. The painting was shown to a sample of n=50 participants, and each was asked to hung the painting in the orientation that looked correct. The following data indicate how many people choose each of the four sides to be placed at the top. Top up (correct) Bottom up fo 18 17 Left side up Right side up 7 8 15 16 17 18 19 Problems The question for the hypothesis test is whether there are any preferences among the four possible orientations. Are any of the orientations selected more (or less) often than would be expected simply by chance? We will set alpha at α =.05 20 Problems Step 1) H : fo=fe no preference for any specific 0 orientation H : fo≠fe 1 preference for specific orientation 21 Step 2 df=C-1 22 23 Problems A researcher is using a chi-square test for independence to examine the relationship between TV preferences and gender for a sample of n = 100 children. Each child is asked to select his/her favorite from a fixed set of three TV shows and each child is classified as male or female. The chi-square statistic for this study would have df equal to ? 24 df= c-1 25 Problems 26 Check your book for the critical values. 27

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