Practice question
SAMPLE/EXAMPLE:
UV .. ONE WAY ANOVA TEST TWO College readiness Does the Rate of Poverty in a School Influence Keystone Math Scores? Use the attached table to get your data. Data source: http://www.paschoolperformance.org Level A1 Level A2 Level A3 Conditions k = High Poverty Medium Poverty Low Poverty X Y2 X X 2 X Y2 23.11 534.07 71.5 $112.25 77.05 5936. 70 12. 31 IS1. SY 80.6 6496. 3 b 106 10 00 0 71.21 5070, 86 82.2 6756.84 10 0 10 00 0 47.62 2267. 66 56.74 3219. 43 106 10 00 0 58.4 7814.56 56.3 316 9.61 10000 89.51 8012.04 50.97 259794 Totals EX = 332.16 EX= 318.3) EX= 477.05 EXtot= 1207. 52 [X2= 23850.74 [X2= 27352.51 [X2= 45936.7 Ex tot= 97139.95 n1= 6 n2= 6 n 3= N = X 1= 55, 36 * 2 = 66.39 X 3= 95.41 K = aHigh School Poverty Level Poverty rate Keystone- College readiness Overall Category Math benchmark Academic score (Created) (based on SAT) 33.75 47.8 Allentown 73.49 23.11 Dieruff 72.85 36.86 12.31 55 74.9 Liberty 56.26 53.89 71.21 HIGH 47.62 59.7 Catasauqua 49.36 73.83 85 Whitehall 48.07 73.54 88.4 Northwest 47.66 31.03 89.51 72.6 Easton 46.57 62.86 71.5 71.54 Freedom 45.19 54.35 80.6 69.5 Wilson 43.22 74.34 82.2 93.6 MEDIUM Northern Lehigh 38.25 37.2 56.74 74.1 37.34 68.92 56.3 82.1 Bangor Pen Argyl 33.33 68.85 50.97 70.3 29.58 74.26 77.05 88.1 Salisbury 24.22 80.5 100 84.8 Emmaus Parkland LOW 22.71 80.79 100 75.6 15.79 86.67 100 98.8 Nazareth 11.18 100 81.1 Southern Lehigh 74.25STEP ONE: STATE HYPOTHESIS (Both Experimental and Statistical) Ha: poverty rate of a school is associated I: notallus arcegod with rate f collage readiness Ho : poverty rate is NOT associated with rate of college readiness Ho: M, = Uz= ML3 STEP TWO: SET UP YOUR SAMPLING DISTRIBUTION Select x 4=05 Locate region of rejection tcrit = 3.74 Determine critical value Need the F-table If bu : k - 1 = 3 - 1 = 2 --use dfon = k -1 and dfwn = N-k to find Foritin the F-table afwn = N-K = 17-3= 14 Computing degrees of freedom Need dfon, dfwn, dftot dfon = k-1 (where k is the number of levels in the factor) d fwn = N-k (where N is total N in the experiment and k is the number of levels in the factor. dftot = N-1 (where N is the total N in the experiment) The F-table: . refer to this link. http://www.stat.purdue.edu/~jtroisi/STAT350Spring2015/tables/FTable.pdf of =. 05 fort = 3.74-8 Region of Rejection fobt = 4:71STEP THREE: COMPUTE F STATISTIC (F-Obtained) You can use this table to help you organize the computations that you need to arrive to the F Statistic. SS df MS F Between 45 74-68 2 2287. 34 4. 71 Within 6794.41 14 485. 32 Tota 1369. 09 16 Formulas MSon 2287.34 Fobt = MSwn 4. 71 4 85. 32 SSon 4574.68 MSon dfon 2 = 2287.34 SSwn z 6794.41 MSwn dfwn T4 - 485. 32 SStot= EXlot- ([Xtot)= = 97139,95- 85 770. 86 = 11369.09 SSon= ( X in column)2 ( [xtot) 2 332 .16 398.31 477.05 1207.52 n in column 17 1103 30.27 + 158650.9 2275 76. 7 1458104. 6 6 SSwn = SStot - SSon 6 S 17 18 39g. 38 + 26441.82+ 45515. 34- 85770, 859 136 9.09- 4 574.68 90 345.53 - 85770. 859 SSwn = 6714.41 SSu: 4 574, 68STEP FOUR: INTERPRET AND REPORT RESULTS Compare Fobt to Forit State whether results are significant or non-significant and report results using standard format. Rejecting Ho, Accepting the Ha. Results are Signifi cant. It is likely that poverity rate in a school affects college readiness. f ( 2, 14 ) = 4.71 , P 2 05 CONDUCT POST HOC TEST (IF APPLICABLE) HSD (Honestly Significant Difference) HSD =) (qk) (MSwn) = 3.7 485. 32 5.67 3.7 / 85. 59 = 3. 7 9 . 25 ) = 34 . 23 n= number of scores in each level of the factor HSD = 34. 23 qk can be obtained on the last page of this packet. Level A1 Level A2 Level A3 significance lies Low poverty Moderate poverty High Poverty between levels A: 6 X1 X 2 x , NaS A, ( low poverity ) 95.41 66.39 5 50 36 and A3 (high poverty ) 29.02 1 1.03 40.05 Determine differences between each pair of means. Subtract each mean from every other mean. Ignore positive or negative because it is a two-tailed test. On the line connecting any two levels is the absolute difference between their means. Compare each difference to the HSD. If the absolute difference between two means is greater than the HSD then these means differ significantly.Post Hoc Test 40% of the change in Effect Size (Eta Squared) College readiness can be 4574. 68 explained by the change 125son SStot = . 40 11369.09 in poverty level . This is the proportion of variance in dependent scores that is accounted for by changing the levels of a factor). Will be between 0 and 1, indicating the extent to which dependent scores change as the independent variable changes . The larger the n the larger the role that factor plays in determining differences.ONE WAY ANOVA TEST TWO Does the Rate of Poverty in a School Influence Keystone Math Scores? Use the attached table to get your data. Data source: http://www.paschoolperformance.org Level A1 Level A2 Level A3 Conditions High Poverty Medium Poverty Low Poverty K = X X 2 X X 2 X X 2 Totals EX = EX= EX= EXtot= EX2= EX2= EX2= Ex tot= n1= n2= n 3= N= X 1= X 2 = X 3= k=High School Poverty Level Poverty rate Keystone- College readiness Overall Category Math benchmark Academic score (Created) (based on SAT) Allentown 73.49 33.75 23.11 47.8 Dieruff 72.85 36.86 12.31 55 71.21 Liberty 56.26 53.89 74.9 HIGH 59.7 Catasauqua 49.36 73.83 47.62 Whitehall 48.07 73.54 88.4 85 Northwest 47.66 31.03 89.51 72.6 46.57 62.86 71.5 71.54 Easton Freedom 45.19 54.35 80.6 69.5 43.22 74.34 82.2 93.6 Wilson MEDIUM Northern Lehigh 38.25 67.2 56.74 74.1 Bangor 37.34 68.92 56.3 82.1 33.33 68.85 50.97 70.3 Pen Argyl 74.26 77.05 88.1 Salisbury 29.58 100 84.8 Emmaus 24.22 80.5 Parkland LOW 22.71 80.79 100 75.6 98.8 Nazareth 15.79 86.67 100 81.1 Southern Lehigh 11.18 74.25 100STEP ONE: STATE HYPOTHESIS (Both Experimental and Statistical) STEP TWO: SET UP YOUR SAMPLING DISTRIBUTION Select x Locate region of rejection Determine critical value Need the F-table --use dfon = k-1 and dfwn = N-k to find Foritin the F-table Computing degrees of freedom Need dfon, dfwn, dftot dfon= k -1 (where k is the number of levels in the factor) dfwn = N-k (where N is total N in the experiment and k is the number of levels in the factor. dftot = N-1 (where N is the total N in the experiment) The F-table: 1.. .. . - refer to this link. http://www.stat.purdue.edu/~jtroisi/STAT350Spring2015/tables/FTable.pdfSTEP THREE: COMPUTE F STATISTIC (F-Obtained) You can use this table to help you organize the computations that you need to arrive to the F Statistic. SS df MS F Between Within Tota Formulas Fobt = M MSon MSwn SSon MSon afon Swn MSwn dfwn SStot= [X? _ (EXtot)2 N SSon= ( 2X in column) (EXtot)2 n in column N SSwn = SStot - SSonSTEP FOUR: INTERPRET AND REPORT RESULTS Compare Fobt to Fm: State whether results are significant or nonsignificant and report results using standard format. CONDUCT POST HOC TEST (IF APPLICABLE) HSD (Honestly Significant Difference) M SW" n HSD = (61k) ( n= number of scores in each level of the factor qk can be obtained on the last page ofthis packet. Determine differences between each pair of means. Subtract each mean from every other mean. Ignore positive or negative because it is a two-tailed test. On the line connecting any two levels is the absolute difference between their means. Compare each difference to the HSD. If the absolute difference between two means is greater than the HSD then these means differ significantly. Effect Size (Eta Squared) r,2 _55bn 55tot This is the proportion of variance in dependent scores that is accounted for by changing the levels of a factor). 0 Will be between 0 and 1, indicating the extent to which dependent scores change as the independent variable changes. 0 The larger the n2 the larger the role thatfactor plays in determining differences
