anova complex design

ANOVA complex design

What is in a results section???

LOOK at the example in your textbook.

You need to have subheading.You need to have figures and they must have useful figure captions.You must refer to your figures.You need to describe the data in some wayYou need to describe the analyses and what you found.Is it significant? Or notThen add some English to describe what you found.

e.gTo examine the effects of memory training on retention of words, 20 college students were randomly assigned to four training conditions (n=5) defined by the instructions to participants: story method, imagery method, rhyme method, and control (no specific instructions). Mean recall out of a possible 20 words (and the sample standard deviation) for each condition was: story 13.2(1.3), imagery 14.4 (1.8), rhyme 13.4 (1.3) and control 10.0 (1.6). Confidence intervals for the means in each group are shown in figure 1. Mean recall differed significantly among the four instruction conditions, F(3,16) = 7.8, p<.05. MS = 240….

A paragraph that describes what is compared and what you found.Where I should look to find the information.

Reporting results of complex design

• What kind of test• description of variables and definitions of levels (conditions) of each• summary statistics for cells in design matrix (figure)• report F tests for main effects and interactions• effect size • statement of power for nonsignificant results• simple main effects analysis when interaction is statistically

significant• description of statistically significant interactions – looking at cell

means• description of statistically significant main effect • analytical comparisons – to clarify sources of systematic variation• conclusion from analysis

The data are from a statement by Texaco, Inc. to the Air and Water Pollution Subcommittee of the Senate Public Works Committee on June 26, 1973. Mr. John McKinley, President of Texaco, cited the Octel filter, developed by Associated Octel Company as effective in reducing pollution. However, questions had been raised about the effects of pollution filters on aspects of vehicle performance, including noise levels. He referred to data presented in the datafile associated with this story as evidence that the Octel filter was was at least as good as a standard silencer in controlling vehicle noise levels.

Car Noise

The data constitute a 3-way factorial experiment with 3 replications.

The factors are type of filter (2 types), vehicle size (3 sizes), and side of car (two sides).

Number of cases = 36

DV

NOISE = Noise level reading (decibels)

IV

SIZE = Vehicle size: 1 small, 2 medium, 3 large TYPE = 1 standard silencer ,2 Octel filter SIDE = 1 right side 2 left side of car

Between-Subjects Factors

small 12medium 12large 12standard 18Octel 18right 18left 18

1.002.003.00

size

1.002.00

type

1.002.00

side

Value Label N

Descriptive Statistics

Dependent Variable: noise

816.6667 5.77350 3835.0000 .00000 3825.8333 10.68488 6820.0000 .00000 3825.0000 .00000 3822.5000 2.73861 6818.3333 4.08248 6830.0000 5.47723 6824.1667 7.63763 12841.6667 2.88675 3850.0000 5.00000 3845.8333 5.84523 6821.6667 2.88675 3821.6667 5.77350 3821.6667 4.08248 6831.6667 11.25463 6835.8333 16.25320 6833.7500 13.50505 12786.6667 2.88675 3763.3333 5.77350 3775.0000 13.41641 6775.0000 .00000 3765.0000 5.00000 3770.0000 6.32456 6780.8333 6.64580 6764.1667 4.91596 6772.5000 10.33529 12815.0000 24.10913 9816.1111 40.29406 9815.5556 32.21659 18805.5556 22.97341 9803.8889 29.45100 9804.7222 25.63730 18810.2778 23.35608 18810.0000 34.81041 18810.1389 29.21561 36

siderightleftTotalrightleftTotalrightleftTotalrightleftTotalrightleftTotalrightleftTotalrightleftTotalrightleftTotalrightleftTotalrightleftTotalrightleftTotalrightleftTotal

typestandard

Octel

Total

standard

Octel

Total

standard

Octel

Total

standard

Octel

Total

sizesmall

medium

large

Total

Mean Std. Deviation N

Tests of Between-Subjects Effects


29524.306a 11 2684.028 184.048 .00023627700.7 1 23627701 1620185 .00026051.389 2 13025.694 893.190 .0001056.250 1 1056.250 72.429 .000

.694 1 .694 .048 .829804.167 2 402.083 27.571 .000

1293.056 2 646.528 44.333 .00017.361 1 17.361 1.190 .286

301.389 2 150.694 10.333 .001350.000 24 14.583

23657575.0 3629874.306 35

SourceCorrected ModelInterceptsizetypesidesize * typesize * sidetype * sidesize * type * sideErrorTotalCorrected Total

Type III Sumof Squares df

MeanSquare F Sig.

R Squared = .988 (Adjusted R Squared = .983)a.



29524.306b 11 2684.028 184.048 .000 .988 2024.524 1.00023627700.7 1 23627700.69 1620185 .000 1.000 1620185.2 1.00026051.389 2 13025.694 893.190 .000 .987 1786.381 1.0001056.250 1 1056.250 72.429 .000 .751 72.429 1.000

.694 1 .694 .048 .829 .002 .048 .055804.167 2 402.083 27.571 .000 .697 55.143 1.000

1293.056 2 646.528 44.333 .000 .787 88.667 1.00017.361 1 17.361 1.190 .286 .047 1.190 .182

301.389 2 150.694 10.333 .001 .463 20.667 .975350.000 24 14.583

23657575.0 3629874.306 35

SourceCorrected ModelInterceptsizetypesidesize * typesize * sidetype * sidesize * type * sideErrorTotalCorrected Total

Type III Sumof Squares df Mean Square F Sig.

Partial EtaSquared

Noncent.Parameter

ObservedPowera

Computed using alpha = .05a.

R Squared = .988 (Adjusted R Squared = .983)b.

Descriptive Statistics


816.6667 5.77350 3835.0000 .00000 3825.8333 10.68488 6820.0000 .00000 3825.0000 .00000 3822.5000 2.73861 6818.3333 4.08248 6830.0000 5.47723 6824.1667 7.63763 12841.6667 2.88675 3850.0000 5.00000 3845.8333 5.84523 6821.6667 2.88675 3821.6667 5.77350 3821.6667 4.08248 6831.6667 11.25463 6835.8333 16.25320 6833.7500 13.50505 12786.6667 2.88675 3763.3333 5.77350 3775.0000 13.41641 6775.0000 .00000 3765.0000 5.00000 3770.0000 6.32456 6780.8333 6.64580 6764.1667 4.91596 6772.5000 10.33529 12815.0000 24.10913 9816.1111 40.29406 9815.5556 32.21659 18805.5556 22.97341 9803.8889 29.45100 9804.7222 25.63730 18810.2778 23.35608 18810.0000 34.81041 18810.1389 29.21561 36

siderightleftTotalrightleftTotalrightleftTotalrightleftTotalrightleftTotalrightleftTotalrightleftTotalrightleftTotalrightleftTotalrightleftTotalrightleftTotalrightleftTotal

typestandard

Octel

Total

standard

Octel

Total

standard

Octel

Total

standard

Octel

Total

sizesmall

medium

large

Total

Mean Std. Deviation N

Main effect Size is significant

Mean small 824.16 sd = 7.63 Mean medium 833.75 sd =13.5Mean large 772.50 sd= 10.33

Need post hoc tests

Main effectType is significant

Standard mean 815.56 sd =32.2Octel mean 804.72 sd =25.63

Don’t need post hoc tests

Multiple Comparisons

Dependent Variable: noiseTukey HSD

-9.5833* 1.55902 .000 -13.4767 -5.690051.6667* 1.55902 .000 47.7733 55.56009.5833* 1.55902 .000 5.6900 13.4767

61.2500* 1.55902 .000 57.3567 65.1433-51.6667* 1.55902 .000 -55.5600 -47.7733-61.2500* 1.55902 .000 -65.1433 -57.3567

(J) sizemediumlargesmalllargesmallmedium

(I) sizesmall

medium

large

MeanDifference

(I-J) Std. Error Sig. Lower Bound Upper Bound95% Confidence Interval

Based on observed means.The mean difference is significant at the .05 level.*.

All sizes differ.

Interaction

Size by Side is significantNeed to find out where is the difference

Simple main effects analysis

Do t-test for the smallAnd one for the mediumAnd one for large

One anova for left sideOne anova for right side

Independent Samples Test

4.000 .073 -4.183 10 .002 -11.66667 2.78887 -17.88065 -5.45268

-4.183 9.245 .002 -11.66667 2.78887 -17.95010 -5.38323

Equal variancesassumedEqual variancesnot assumed

noiseF Sig.

Levene's Test forEquality of Variances

t df Sig. (2-tailed)Mean

DifferenceStd. ErrorDifference Lower Upper

95% ConfidenceInterval of the

Difference

t-test for Equality of Means


2.500 .145 4.939 10 .001 16.66667 3.37474 9.14727 24.18606

4.939 9.211 .001 16.66667 3.37474 9.05904 24.27430


noiseF Sig.





Difference


m

L

s

side


3.472 .092 -.516 10 .617 -4.16667 8.07087 -22.14968 13.81634

-.516 8.899 .618 -4.16667 8.07087 -22.45600 14.12266


noiseF Sig.





Difference


• Small size left bigger than right

• Medium size no difference

• Large size right bigger than left

ANOVA

noise

8336.111 2 4168.056 66.689 .000937.500 15 62.500

9273.611 17

Between GroupsWithin GroupsTotal

Sum ofSquares df Mean Square F Sig.

Right



-13.33333* 4.56435 .027 -25.1891 -1.477637.50000* 4.56435 .000 25.6442 49.355813.33333* 4.56435 .027 1.4776 25.189150.83333* 4.56435 .000 38.9776 62.6891

-37.50000* 4.56435 .000 -49.3558 -25.6442-50.83333* 4.56435 .000 -62.6891 -38.9776


(I) sizesmall

medium

large

MeanDifference


The mean difference is significant at the .05 level.*.

ANOVA

noise

19008.333 2 9504.167 89.568 .0001591.667 15 106.111

20600.000 17





-5.83333 5.94730 .600 -21.2813 9.614665.83333* 5.94730 .000 50.3854 81.28135.83333 5.94730 .600 -9.6146 21.2813

71.66667* 5.94730 .000 56.2187 87.1146-65.83333* 5.94730 .000 -81.2813 -50.3854-71.66667* 5.94730 .000 -87.1146 -56.2187


(I) sizesmall

medium

large

MeanDifference



Left

• On right - small cars louder than large - medium cars louder than large - small cars quieter than medium

• On left - small cars louder than large - medium cars louder than large

Interaction

Size by Type is significantNeed to find out where is the difference

Simple main effects analysis

Do t-test for the smallAnd one for the mediumAnd one for large

One for type standardOne for type Octel


10.000 .010 .826 10 .428 5.00000 6.05530 -8.49205 18.49205

.826 7.118 .436 5.00000 6.05530 -9.27067 19.27067


noiseF Sig.





Difference



.537 .481 8.303 10 .000 24.16667 2.91071 17.68120 30.65213

8.303 8.940 .000 24.16667 2.91071 17.57549 30.75784


noiseF Sig.





Difference



20.000 .001 .740 10 .476 3.33333 4.50309 -6.70017 13.36683

.740 5.654 .489 3.33333 4.50309 -7.85080 14.51746


noiseF Sig.





Difference


s

m

L

Standard

ANOVA

noise

16002.778 2 8001.389 73.109 .0001641.667 15 109.444

17644.444 17





-20.00000* 6.03999 .012 -35.6887 -4.311350.83333* 6.03999 .000 35.1446 66.522020.00000* 6.03999 .012 4.3113 35.688770.83333* 6.03999 .000 55.1446 86.5220

-50.83333* 6.03999 .000 -66.5220 -35.1446-70.83333* 6.03999 .000 -86.5220 -55.1446


(I) sizesmall

medium

large

MeanDifference



ANOVA

noise

16002.778 2 8001.389 73.109 .0001641.667 15 109.444

17644.444 17





-20.00000* 6.03999 .012 -35.6887 -4.311350.83333* 6.03999 .000 35.1446 66.522020.00000* 6.03999 .012 4.3113 35.688770.83333* 6.03999 .000 55.1446 86.5220

-50.83333* 6.03999 .000 -66.5220 -35.1446-70.83333* 6.03999 .000 -86.5220 -55.1446


(I) sizesmall

medium

large

MeanDifference



Octel

significant 3-way interaction.

Size by type by side

Need to separate the factors so can do2-way analyses

Hold one factor constant and test otherEg do a 2X2 of small cars2X2 of medium and 2X2 of large….

Small car – type by side

Test small car



575.000b 3 191.667 23.000 .000 .896 69.000 1.0008151008.333 1 8151008.333 978121.0 .000 1.000 978121.000 1.000

33.333 1 33.333 4.000 .081 .333 4.000 .421408.333 1 408.333 49.000 .000 .860 49.000 1.000133.333 1 133.333 16.000 .004 .667 16.000 .93766.667 8 8.333

8151650.000 12641.667 11

SourceCorrected ModelIntercepttypesidetype * sideErrorTotalCorrected Total


Partial EtaSquared

Noncent.Parameter

ObservedPowera



Side is significant - left bigger than rightInteraction is significant

Small car Type : t –tests for the interaction Right


16.000 .016 -1.000 4 .374 -3.33333 3.33333 -12.58815 5.92148

-1.000 2.000 .423 -3.33333 3.33333 -17.67551 11.00884


noiseF Sig.





Difference


Group Statistics

3 835.0000 .00000a .000003 825.0000 .00000a .00000

typestandardOctel

noiseN Mean Std. Deviation

Std. ErrorMean

t cannot be computed because the standard deviations of bothgroups are 0.

a.

Left

Octel louder than standard

Small car – t-tests for side


16.000 .016 -5.500 4 .005 -18.33333 3.33333 -27.58815 -9.07852

-5.500 2.000 .032 -18.33333 3.33333 -32.67551 -3.99116


noiseF Sig.





Difference


Standard

Octel

Group Statistics

3 820.0000 .00000a .000003 825.0000 .00000a .00000

siderightleft

noiseN Mean Std. Deviation

Std. ErrorMean

t cannot be computed because the standard deviations of bothgroups are 0.

a.

Left louder than right

Medium car - type by side

Test Medium car



1856.250b 3 618.750 33.000 .000 .925 99.000 1.0008341668.750 1 8341668.750 444889.0 .000 1.000 444889.000 1.000

1752.083 1 1752.083 93.444 .000 .921 93.444 1.00052.083 1 52.083 2.778 .134 .258 2.778 .31252.083 1 52.083 2.778 .134 .258 2.778 .312

150.000 8 18.7508343675.000 12

2006.250 11



Partial EtaSquared

Noncent.Parameter

ObservedPowera



Type is significant – standard louder than Octel

Large car – type by side

Test large car



1041.667b 3 347.222 20.833 .000 .887 62.500 1.0007161075.000 1 7161075.000 429664.5 .000 1.000 429664.500 1.000

75.000 1 75.000 4.500 .067 .360 4.500 .463833.333 1 833.333 50.000 .000 .862 50.000 1.000133.333 1 133.333 8.000 .022 .500 8.000 .698133.333 8 16.667

7162250.000 121175.000 11



Partial EtaSquared

Noncent.Parameter

ObservedPowera



Side is significant – right is louder than leftInteraction is significant -

Large car Type : t –tests for the interactionRight

Left


16.000 .016 7.000 4 .002 11.66667 1.66667 7.03926 16.29408

7.000 2.000 .020 11.66667 1.66667 4.49558 18.83775


noiseF Sig.





Difference



.308 .609 -.378 4 .725 -1.66667 4.40959 -13.90964 10.57631

-.378 3.920 .725 -1.66667 4.40959 -14.00881 10.67548


noiseF Sig.





Difference


Standard louder than octel


3.200 .148 6.261 4 .003 23.33333 3.72678 12.98613 33.68053

6.261 2.941 .009 23.33333 3.72678 11.33773 35.32894


noiseF Sig.





Difference


Standard

Octel


4.000 .116 3.464 4 .026 10.00000 2.88675 1.98509 18.01491

3.464 2.000 .074 10.00000 2.88675 -2.42069 22.42069


noiseF Sig.





Difference


anova complex design

Documents

vehicle size

octel filter

mean medium

car main effect size

rightmedium size

differencelarge size

right sidemlssidesmall

mean recall