StudyProblemsCh10

StudyProblemsCh10 - I J G A L O A L O A L O Chapter 10:...

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Unformatted text preview: I J G A L O A L O A L O Chapter 10: Analysis of Variance A L O A L O 1. What general form does the alternative hypothesis take in Analysis of Variance? A L O 2. If you reject the null hypothesis in Analysis of Variance, what can you conclude (without running any additional post hoc testing)? 3." M&%&( &$( ;*1&1;%+ 2%+9( -, between-groups variability and within-groups ,-* %) %+4$% In L Distinguish between C ,-* % -)(67%3 8(&7(()6098:(;& %)%+3010 -, 2%*1%);( variability. research design, what contributes to each? +(2(+ -, "EL 9)/(* (%;$ -, &$( ,-++-71)' ;-)/1&1-)0K I" % N AD ) N O J" % N FD ) N L G" % N AD ) N of a. Number !E groups = 3; number of scores per group = 7 @" % N LD ) N P 4. Determine the critical value for alpha = .05 and each of the following conditions: b. Number of groups = 4; number of scores per group = 5 5. If you ran Analysis of Variance using alpha of .01 instead of the typical .05 level, would the rejection region be larger and smaller? Would the critical value be higher or lower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` 4 ` `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nswers: 3-:", 2+3:#& A.+(.-@;,130)/),.)8.*.+# 71-7",-2 +(" /),.)8.*.+# 1< 271,"2 )," ) -348",1< +(" ;,1302 )-1+(",& 6+ 7)--1+ 8" 2344),.9": .- 2.-;*" 4)+("4)+.7)* 2+)+"4"-+ 8"7)32" +("," =.+(.- ")7( 1< ;,1302& =)#2 .- =(.7( +(,"" 1, 41," 0103*)+.1- 4")-2 7)- 0)++",- +("42"*/"2 21 +()+ +("# )," -1+ )** "53)*& 1.The alternative hypothesis states that not all population means are equal. This is all that is necessary to reject the null hypothesis (that all population means are equal). In other words, at B&'(" C ,)+.1D /),.)8.*.+# ,3-D =.** )00,1)7( %&EE 8"+=""- +(" (#01+("2.2 .2 +,3"& '(" C ,)+.1D >&?"+=""-@;,1301/", +(" *1-;differ. least two population means 71-7",-2 +(" :.<<","-7"2 =("- +(" -3** 4")- 271,"2 .- +(" /),.132 1/", +(" *1-; ,3-D =.** 8" ;,")+", +()- %&EE 71-7",-2 +(" (#01+("2.2 .2 -1+ +,3"& ;,1302 3-:", 2+3:#& A.+(.-@;,130 /),.)8.*.+# =("- +(" -3**/),.)8.*.+# 1< 271,"2 =.+(.- ")7( 1< +(" 2.;,1302& Rejecting the null hypothesis tells you simply that at least two groups come from different populations, 1< +(" 234to a statistically significant degree. This process does not specify how F&'(" /)*3" or, differ 1< 253),"2 =.+(.- 432+ 8" E 8"7)32" )** 271,"2 =.+(.- ) ;./"- ;,130 )," +(" many groups differ, nor which specific groups differ. This is because the numerator in the F2)4"& B&'(" captures the overall amount of between-groups variability, not on +,3"& '(" C ,)+.1D ratio C ,)+.1D 1/", +(" *1-; ,3-D =.** )00,1)7( %&EE =("- +(" -3** (#01+("2.2 .2 a pairwise basis. 1/", +(" *1-; ,3-D =.** 8" ;,")+", +()- %&EE =("- +(" -3** (#01+("2.2 .2 -1+ +,3"& G& 3. The extent to which the various groups in your independent variable differ from one another is b'(")/)*3":<H +(" 234 1< @% I> Within-groups variability )** how much individuals in a given group etween-groups@ variability. =.+(.- 432+ 8" E 8"7)32" is 271,"2 =.+(.- ) ;./"- ;,130 )," +(" F& H& I BD 1< I ) % I B 253),"2 differ from I ) L other. 2)4"& I JD Keach - I B L J I >% :<M,,1, I K @ ) I >% @ B I %N 4. Determine critical values. First, you need to calculate the degrees of freedom for the G& '("- *11O and denominator +"Q+811O the F ratio. numerator (df ) )+ ')8*" P& B) .- #13,(df ) of+1 <.-: +(" 7,.+.7)* /)*3" 1< CD =(.7( .2 B&GG A error H& ) I BD :<H I ) @ % I B @% I> ?& I FD :<H I ) @ B L J @% IB - I)JD K I ) L - I % I F I >% - I GD K L - @ F L %N :<M,,1, I K @I))I >% I B I G I >E :< *11O K @ ) I P& B) I #13, '("- M,,1, I )+ ')8*">E @ F .- %R +"Q+811O +1 <.-: +(" 7,.+.7)* /)*3" 1< CD =(.7( .2 B&GG P,.+.7)* /)*3" I B&>F ?& ) I FD :<H I ) @ % I F @% IB P& GD I I - I:<H K > ) L - I F L G I >E :<M,,1, K @ ) :<M,,1, I I >J I >E @ F I %R P,.+.7)* /)*3" I B&BG P,.+.7)* /)*3" I B&>F :< I I 5.P& S&H:<H> Fof .01 compared to .05, the rejection region is smaller, comprising only 1% of At alpha :<I >J :<M,,1, M,,1, F test possible I FE statistics. The critical value is higher, which places it further out in the P,.+.7)* /)*3" I tail end /)*3" I B&BG>&R% P,.+.7)* of the distribution of test statistics. 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This note was uploaded on 10/26/2011 for the course SLL 330 taught by Professor Damare during the Spring '10 term at USC.

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