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F = MS bet MS within

By Joanne Hunt,2014-06-18 21:59
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F = MS bet MS within

F = MS bet / MS within

    Step 1: Sum columns & get ?X? total, ?X total & Group Means

    Social Class & IQ

    Upper Class (N=5) Middle (N=5) Lower (N=5)

     X1 X1? X2 X2? X3 X3?

     130 16,900 120 14,400 110 12,100

     125 15,625 115 13,225 100 10,000

     130 16,900 115 13,225 90 8,100 120 14,400 110 12,100 100 10,000

     122 14,884 112 12,544 85 7,225 _____________ ______________ _______________ ?X1=627 ?X1? =78,709 ?X2=572 ?X2? =65,494 ?X3=48 ?X3? =47,425

Total N= 15

    ?X? total = 78,709 + 65,494 + 47,425 = 191,628

?X total = 627 + 572 + 485 = 1,684

Mean, Group 1 = 627/5 = 125.4

    Mean, Group 2 = 572/5 = 114.4

    Mean, Group 3 = 485/5 = 97.0

Step 2: Total Sum of Squares

    SS total = ?X? total - (?X total)? / N total

SS total = 191,628 (1,684)? / 15

SS total = 191,628 2,835,856 / 15

SS total = 191,628 189,057.07

SS total = 2,570.93

Step 3: Between Groups Sum of Squares

    SS between = [? (?X)? / N ] (?X total)? / N total

    SS between = [ (627)? / 5 + (572)? /5 + (485)? /5] (1,684)? / 15

    SS between = ( 393,129 / 5 + 327,184 / 5 + 235,225/5) 2,835,856 /15

    SS between = (78,625.8 + 65,436.8 + 47,045.0) 189,057.07

SS between = 191,107.60 189,057.07

SS between = 2,050.53

Step 4: Within Group Sum of Squares

SS within = SS total SS bet

SS within = 2,570.93 2,050.52

SS within = 520.40

Step 5: Find between group degrees of freedom

df between = K (# of groups) 1

df = 3 (upper, middle, and lower class) 1 = 2

Step 6: Find within-groups degrees of freedom

df within = Ntotal k (# of groups)

df within = 15 3 = 12

    Remember that F = MS bet / MS within

Step 7: MS Between (Between-group mean square)

    MS between = SS between / df between

    Ms between = 2050.53 / 2 = 1025.27

Step 8: Find MS Within (Within-group mean square)

    MS within = SS within / df within

    MS within = 520.40 / 12 = 43.37

Step 9: Calculate the F ratio

F = 1025.27 / 43.37

    F = 23.64

Step 10: Compare calculated F to critical F in the table

Table F = 3.88 at alpha level = .05, df 2 & 12

DECISON? Do we reject Ho?

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