Variance Test

Question 1

SD & Dispersion

Answer 1

• Some more descriptive stats include DISPERSION, divided into variance (average distance/squared dif from mean) and interquartile range; same mean, but the dispersion around it changes. STANDARD DEVIATION is the SQUARE ROOT of VARIANCE.

Question 2

Variance (EG)

Answer 2

o Ie. Effects of teaching programme on exam performance. Is there a dif?
o TUTORIALS: 65, 96, 84, 30, 27=60.4
o LECTURES: 64, 60, 47, 76, 55=60.4
o Identical means but dif variabilities.
- Sample variance also under-estimates pop variance (biased estimates)

Question 3

Calc Variance

Answer 3

o^2=E(X-X_)^2/N

Question 4

Calc Variance (Biased Estimates) 1

Answer 4

o 1. POP OF 3 NUM
o 1, 2, 3; mean=2
o o^2=E(X-X_)^2/N
o pop variance=2/3=.67

Question 5

Calc Variance (Biased Estimates) 2

Answer 5

o 2. ESTIMATE N=2 POP VARIANCE

o Pop variance = .33

Question 6

Calc Variance (Biased Estimates) 3

Answer 6

o 3. FIX
o S^2= E(X-X_)^2/N-1
o = .67, so UNBIASED.

Question 7

Calc Variance 1

Answer 7

o	1. LECTURES
o	S^2= E(X-X_)^2/N-1
o	(X-X_)=3.6, -0.4, -13.4, 15.6, -5.4
o	(X-X_)^2= 12.96, .16, 179.6, 243.4, 29.16
o	E(X-X_)^2= 465.2
o	E(X-X_)^2/N-1=465.2/5-1
o	S^2=116.3

Question 8

Calc Variance 2

Answer 8

o	2. TUTORIALS
o	(X-X_)=4.6, 35.6, 23.6, -30.4, -33.4
o	(X-X_)^2=21.16, 1267.36, 556.96, 924.16, 1115.56
o	E(X-X_)^2= 3885.20
o	E(X-X_)^2/N-1= 3885.20/5-1
o	S^2=971.30

Question 9

Inferential Stats

Answer 9

• The likelihood of 2 variances being the same can be quantified probabilistically; group difs in central tendency (WRS) and variability (variance test (NOT CALC!))

Question 10

Variance

Answer 10

F=S^2H/S^2L

Question 11

Variance 1

Answer 11

o 1. DIVIDE BIG VARIANCE BY SMALL
o 971.3/116.3
o F=8.35

Question 12

Variance 2

Answer 12

o	2. STATSIG IF F>CV
o	DF=N-1 (as in every variance)
o	F=8.35; CV=6.39
o	8.35>6.39
o	STATSIG! 
o	There is a sig dif in var between tut/lec with performance after tuts being more variable than after lecs.