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

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 12

medium 12

large 12

standard 18

Octel 18

right 18

left 18

1.00

2.00

3.00

size

1.00

2.00

type

1.00

2.00

side

Value Label N

Descriptive Statistics

Dependent Variable: noise

816.6667 5.77350 3

835.0000 .00000 3

825.8333 10.68488 6

820.0000 .00000 3

825.0000 .00000 3

822.5000 2.73861 6

818.3333 4.08248 6

830.0000 5.47723 6

824.1667 7.63763 12

841.6667 2.88675 3

850.0000 5.00000 3

845.8333 5.84523 6

821.6667 2.88675 3

821.6667 5.77350 3

821.6667 4.08248 6

831.6667 11.25463 6

835.8333 16.25320 6

833.7500 13.50505 12

786.6667 2.88675 3

763.3333 5.77350 3

775.0000 13.41641 6

775.0000 .00000 3

765.0000 5.00000 3

770.0000 6.32456 6

780.8333 6.64580 6

764.1667 4.91596 6

772.5000 10.33529 12

815.0000 24.10913 9

816.1111 40.29406 9

815.5556 32.21659 18

805.5556 22.97341 9

803.8889 29.45100 9

804.7222 25.63730 18

810.2778 23.35608 18

810.0000 34.81041 18

810.1389 29.21561 36

sideright

left

Total

right

left

Total

right

left

Total

right

left

Total

right

left

Total

right

left

Total

right

left

Total

right

left

Total

right

left

Total

right

left

Total

right

left

Total

right

left

Total

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 .000

23627700.7 1 23627701 1620185 .000

26051.389 2 13025.694 893.190 .000

1056.250 1 1056.250 72.429 .000

.694 1 .694 .048 .829

804.167 2 402.083 27.571 .000

1293.056 2 646.528 44.333 .000

17.361 1 17.361 1.190 .286

301.389 2 150.694 10.333 .001

350.000 24 14.583

23657575.0 36

29874.306 35

SourceCorrected Model

Intercept

size

type

side

size * type

size * side

type * side

size * type * side

Error

Total

Corrected 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 1.000

23627700.7 1 23627700.69 1620185 .000 1.000 1620185.2 1.000

26051.389 2 13025.694 893.190 .000 .987 1786.381 1.000

1056.250 1 1056.250 72.429 .000 .751 72.429 1.000

.694 1 .694 .048 .829 .002 .048 .055

804.167 2 402.083 27.571 .000 .697 55.143 1.000

1293.056 2 646.528 44.333 .000 .787 88.667 1.000

17.361 1 17.361 1.190 .286 .047 1.190 .182

301.389 2 150.694 10.333 .001 .463 20.667 .975

350.000 24 14.583

23657575.0 36

29874.306 35


Intercept

size

type

side

size * type

size * side

type * side

size * type * side

Error

Total

Corrected Total

Type III Sumof Squares df Mean Square F Sig.

Partial EtaSquared

Noncent.Parameter

ObservedPower

a

Computed using alpha = .05a.

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

Descriptive Statistics


816.6667 5.77350 3

835.0000 .00000 3

825.8333 10.68488 6

820.0000 .00000 3

825.0000 .00000 3

822.5000 2.73861 6

818.3333 4.08248 6

830.0000 5.47723 6

824.1667 7.63763 12

841.6667 2.88675 3

850.0000 5.00000 3

845.8333 5.84523 6

821.6667 2.88675 3

821.6667 5.77350 3

821.6667 4.08248 6

831.6667 11.25463 6

835.8333 16.25320 6

833.7500 13.50505 12

786.6667 2.88675 3

763.3333 5.77350 3

775.0000 13.41641 6

775.0000 .00000 3

765.0000 5.00000 3

770.0000 6.32456 6

780.8333 6.64580 6

764.1667 4.91596 6

772.5000 10.33529 12

815.0000 24.10913 9

816.1111 40.29406 9

815.5556 32.21659 18

805.5556 22.97341 9

803.8889 29.45100 9

804.7222 25.63730 18

810.2778 23.35608 18

810.0000 34.81041 18

810.1389 29.21561 36

sideright

left

Total

right

left

Total

right

left

Total

right

left

Total

right

left

Total

right

left

Total

right

left

Total

right

left

Total

right

left

Total

right

left

Total

right

left

Total

right

left

Total

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


Tukey HSD

-9.5833* 1.55902 .000 -13.4767 -5.6900

51.6667* 1.55902 .000 47.7733 55.5600

9.5833* 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) sizemedium

large

small

large

small

medium

(I) sizesmall

medium

large

MeanDifference

(I-J) Std. Error Sig. Lower Bound Upper Bound

95% 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 variancesassumed

Equal 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 .000

937.500 15 62.500

9273.611 17

Between Groups

Within Groups

Total

Sum ofSquares df Mean Square F Sig.

Right



Tukey HSD

-13.33333* 4.56435 .027 -25.1891 -1.4776

37.50000* 4.56435 .000 25.6442 49.3558

13.33333* 4.56435 .027 1.4776 25.1891

50.83333* 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

(J) sizemedium

large

small

large

small

medium

(I) sizesmall

medium

large

MeanDifference




ANOVA

noise

19008.333 2 9504.167 89.568 .000

1591.667 15 106.111

20600.000 17

Between Groups

Within Groups

Total




Tukey HSD

-5.83333 5.94730 .600 -21.2813 9.6146

65.83333* 5.94730 .000 50.3854 81.2813

5.83333 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

(J) sizemedium

large

small

large

small

medium

(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 .000

1641.667 15 109.444

17644.444 17

Between Groups

Within Groups

Total




Tukey HSD

-20.00000* 6.03999 .012 -35.6887 -4.3113

50.83333* 6.03999 .000 35.1446 66.5220

20.00000* 6.03999 .012 4.3113 35.6887

70.83333* 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

(J) sizemedium

large

small

large

small

medium

(I) sizesmall

medium

large

MeanDifference




ANOVA

noise

16002.778 2 8001.389 73.109 .000

1641.667 15 109.444

17644.444 17

Between Groups

Within Groups

Total




Tukey HSD

-20.00000* 6.03999 .012 -35.6887 -4.3113

50.83333* 6.03999 .000 35.1446 66.5220

20.00000* 6.03999 .012 4.3113 35.6887

70.83333* 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

(J) sizemedium

large

small

large

small

medium

(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 1.000

8151008.333 1 8151008.333 978121.0 .000 1.000 978121.000 1.000

33.333 1 33.333 4.000 .081 .333 4.000 .421

408.333 1 408.333 49.000 .000 .860 49.000 1.000

133.333 1 133.333 16.000 .004 .667 16.000 .937

66.667 8 8.333

8151650.000 12

641.667 11


Intercept

type

side

type * side

Error

Total

Corrected Total


Partial EtaSquared

Noncent.Parameter

ObservedPower

a



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 .00000

3 825.0000 .00000a .00000

typestandard

Octel

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 .00000

3 825.0000 .00000a .00000

sideright

left

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 1.000

8341668.750 1 8341668.750 444889.0 .000 1.000 444889.000 1.000

1752.083 1 1752.083 93.444 .000 .921 93.444 1.000

52.083 1 52.083 2.778 .134 .258 2.778 .312

52.083 1 52.083 2.778 .134 .258 2.778 .312

150.000 8 18.750

8343675.000 12

2006.250 11


Intercept

type

side

type * side

Error

Total

Corrected Total


Partial EtaSquared

Noncent.Parameter

ObservedPower

a



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 1.000

7161075.000 1 7161075.000 429664.5 .000 1.000 429664.500 1.000

75.000 1 75.000 4.500 .067 .360 4.500 .463

833.333 1 833.333 50.000 .000 .862 50.000 1.000

133.333 1 133.333 8.000 .022 .500 8.000 .698

133.333 8 16.667

7162250.000 12

1175.000 11


Intercept

type

side

type * side

Error

Total

Corrected Total


Partial EtaSquared

Noncent.Parameter

ObservedPower

a



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


Documents

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