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Satterthwaite’s Approximation for Degrees of Freedom Art Instruction Effect on Reading Development J.C. Mills (1973), “The Effect of Art Instruction Upon a Reading Development Test: An Experimental Study with Rural Appalachian Children,” Studies in Art Education, Vol. 14, #3, pp.4-8

Satterthwaite’s Approximation for Degrees of Freedom Art Instruction Effect on Reading Development J.C. Mills (1973), “The Effect of Art Instruction Upon

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Page 1: Satterthwaite’s Approximation for Degrees of Freedom Art Instruction Effect on Reading Development J.C. Mills (1973), “The Effect of Art Instruction Upon

Satterthwaite’s Approximation for Degrees of Freedom

Art Instruction Effect on Reading Development

J.C. Mills (1973), “The Effect of Art Instruction Upon a Reading Development Test: An Experimental Study with Rural Appalachian Children,” Studies in Art Education, Vol. 14, #3, pp.4-8

Page 2: Satterthwaite’s Approximation for Degrees of Freedom Art Instruction Effect on Reading Development J.C. Mills (1973), “The Effect of Art Instruction Upon

Setting • Comparing Means from 2 Normal Distributions• Small Samples (Computer Packages Solve for any sizes)• Distributions have Possibly Different Variances

Page 3: Satterthwaite’s Approximation for Degrees of Freedom Art Instruction Effect on Reading Development J.C. Mills (1973), “The Effect of Art Instruction Upon

Case 1 – Variances are Equal

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Page 4: Satterthwaite’s Approximation for Degrees of Freedom Art Instruction Effect on Reading Development J.C. Mills (1973), “The Effect of Art Instruction Upon

Case 2 – Variances are Unequal - I

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freedom. of degrees itsby divided square-chi a NOT is which *

:consider, variancesestimatedr with Denominato Replacing :Problem

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Page 5: Satterthwaite’s Approximation for Degrees of Freedom Art Instruction Effect on Reading Development J.C. Mills (1973), “The Effect of Art Instruction Upon

Case 2 – Variances are Unequal - II

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2 2 22 2* 1 1 2 21 2

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24 4 2 21 2 1 2

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21 12

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Replacing the unknown variance

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s with their estimates:

1* where: 1

1 1

So, we have the approximate degrees of freedom if our denominator

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n ng MS S n

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were the square root

of the ratio of a chi-square to its degrees of freedom

Page 6: Satterthwaite’s Approximation for Degrees of Freedom Art Instruction Effect on Reading Development J.C. Mills (1973), “The Effect of Art Instruction Upon

Example – Art Instruction Effect on Reading

• Experiment to Determine Effect of Art Instruction on a Reading Development Test 52 Children Given Baseline Reading Test 26 Received Art Instruction (Trt), 26 Did not (Control) Y=Post-Test – Pre-Test Score

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