Anova presentation
ANALYSIS OF
VARIANCE?
WHAT NULL HYPOTHESIS
ISTESTED BY ANOVA?
ANALYSIS OF VARIANCE IS A STATISTICAL METHOD USED TO
TEST DIFFERENCES BETWEEN TWO OR MORE MEANS.
IT IS USED TO TEST GENERAL RATHER THAN SPECIFIC
DIFFERENCES AMONG MEANS. THUS THE NULL HYPOTHESIS IS
CALLED AN OMNIBUS NULL HYPOTHESIS IT MEANS THAT AT
LEAST ONE POPULATION MEAN IS DIFFERENT FROM AT
LEASTONE OTHER MEAN.
THE ANOVA DOES NOT REVEAL WHICH PAIR IS SIGNIFICANT,
THUS A FOLLOW UP TEST IS NECESSARY TO DETERMINEWHICH
PAIR IS DIFFERENT FROM EACH OTHER.
ASSUMPTIONS
1.
THE POPULATION HAVE THE SAME
VARIANCE. THE ASSUMPTION IS CALLED
ASSUMPTION OF HOMOGENEITY OF
VARIANCE.
2.
THE POPULATION ARE NORMALLY
DISTRIBUTED
3.
EACH VALUE IS SAMPLED
INDEPENDENTLY
WHAT IS MEAN SQUARE WITHIN?
Mean
square Within is the value that estimate the population variances of each group( considering that the groups are homogenous as stated in the assumption.
Formula:
WHAT IS MEAN SQUARE
BETWEEN?
MEAN
SQUARE BETWEEN IS AN
ESTIMATOR OF THE POPULATION
VARIANCE IF THE PPULATION
MEANS ARE EQUAL. IF THE MEANS
ARE NOT EQUAL IT ESTIMATES A
LARGER QUANTITY.
Formula:
= / (n-1)
FACTORS AND LEVELS
FACTOR
– A CHARACTERISTIC
UNDER CONSIDERATION, THOUGHT
TO INFLUENCE THE MEASURED
OBSERVATIONS.
LEVEL
– A VALUE OF THE FACTOR.
NE WAY ( FACTOR) ANOVA
IN GENERAL ONE WAY ANOVA TECHNIQUES CAN BE USED TO
STUDY THE EFFECT OF K (>2) LEVELS OF A SINGLE FACTOR
EXAMPLE:
THE TABLE SHOWS THE LIFETIMES UNDER CONTROLLED
CONDITIONS,IN HOURS IN EXCSS OF 1000 HRS, OF SAMPLES OF
60w ELECTRIC LIGHT BULBS OF THREE DIFFERENT BRAND
BRAND
1
2
3
16
18
26
15
22
31
13
20
24
21
16
30
14
24
24
SUMMARIZE DATA
BRAND
1
2
3
SAMPLE SIZE
5
5
5
SUM
80
100
135
SUM OF
SQUARES
1316
2040
3689
MEAN
16
20
27
VARIANCE
9
10
11
SINCE EACH OF THESE THREE SAMPLE VARIANCES IS AN
ESTIMATE OF THECOMMON POPULATION VARIANCE . A POOLED
ESTIMATE MAY BE CALCULATED IN THE USUAL WAY.
=
VARIANCE?
WHAT NULL HYPOTHESIS
ISTESTED BY ANOVA?
ANALYSIS OF VARIANCE IS A STATISTICAL METHOD USED TO
TEST DIFFERENCES BETWEEN TWO OR MORE MEANS.
IT IS USED TO TEST GENERAL RATHER THAN SPECIFIC
DIFFERENCES AMONG MEANS. THUS THE NULL HYPOTHESIS IS
CALLED AN OMNIBUS NULL HYPOTHESIS IT MEANS THAT AT
LEAST ONE POPULATION MEAN IS DIFFERENT FROM AT
LEASTONE OTHER MEAN.
THE ANOVA DOES NOT REVEAL WHICH PAIR IS SIGNIFICANT,
THUS A FOLLOW UP TEST IS NECESSARY TO DETERMINEWHICH
PAIR IS DIFFERENT FROM EACH OTHER.
ASSUMPTIONS
1.
THE POPULATION HAVE THE SAME
VARIANCE. THE ASSUMPTION IS CALLED
ASSUMPTION OF HOMOGENEITY OF
VARIANCE.
2.
THE POPULATION ARE NORMALLY
DISTRIBUTED
3.
EACH VALUE IS SAMPLED
INDEPENDENTLY
WHAT IS MEAN SQUARE WITHIN?
Mean
square Within is the value that estimate the population variances of each group( considering that the groups are homogenous as stated in the assumption.
Formula:
WHAT IS MEAN SQUARE
BETWEEN?
MEAN
SQUARE BETWEEN IS AN
ESTIMATOR OF THE POPULATION
VARIANCE IF THE PPULATION
MEANS ARE EQUAL. IF THE MEANS
ARE NOT EQUAL IT ESTIMATES A
LARGER QUANTITY.
Formula:
= / (n-1)
FACTORS AND LEVELS
FACTOR
– A CHARACTERISTIC
UNDER CONSIDERATION, THOUGHT
TO INFLUENCE THE MEASURED
OBSERVATIONS.
LEVEL
– A VALUE OF THE FACTOR.
NE WAY ( FACTOR) ANOVA
IN GENERAL ONE WAY ANOVA TECHNIQUES CAN BE USED TO
STUDY THE EFFECT OF K (>2) LEVELS OF A SINGLE FACTOR
EXAMPLE:
THE TABLE SHOWS THE LIFETIMES UNDER CONTROLLED
CONDITIONS,IN HOURS IN EXCSS OF 1000 HRS, OF SAMPLES OF
60w ELECTRIC LIGHT BULBS OF THREE DIFFERENT BRAND
BRAND
1
2
3
16
18
26
15
22
31
13
20
24
21
16
30
14
24
24
SUMMARIZE DATA
BRAND
1
2
3
SAMPLE SIZE
5
5
5
SUM
80
100
135
SUM OF
SQUARES
1316
2040
3689
MEAN
16
20
27
VARIANCE
9
10
11
SINCE EACH OF THESE THREE SAMPLE VARIANCES IS AN
ESTIMATE OF THECOMMON POPULATION VARIANCE . A POOLED
ESTIMATE MAY BE CALCULATED IN THE USUAL WAY.
=