ANALYSIS OF
VARIANCE?
WHAT NULL SPECULATION
ISTESTED BY SIMPLY ANOVA?
ANALYSIS OF VARIANCE IS A STATISTICAL APPROACH USED TO
EVALUATION DIFFERENCES BETWEEN TWO OR MORE MEANS.
IT REALLY IS USED TO EVALUATION GENERAL RATHER THAN SPECIFIC
DISSIMILARITIES AMONG MEANS. THUS THE NULL HYPOTHESIS IS
CALLED AN OMNIBUS NULL HYPOTHESIS IT MEANS THAT AT
LEAST ONE INHABITANTS MEAN DIFFERS FROM THE OTHERS FROM FOR
LEASTONE VARIOUS OTHER MEAN.
THE ANOVA DOES NOT EXPOSE WHICH COUPLE IS SIGNIFICANT,
THUS A FOLLOW UP CHECK IS NECESSARY TO DETERMINEWHICH
MATCH IS DIFFERENT FROM EACH OTHER.
PRESUMPTIONS
1 .
THE POPULATION HAVE SIMILAR
VARIANCE. THE ASSUMPTION IS NAMED
ASSUMPTION OF HOMOGENEITY OF
VARIANCE.
2 .
THE PEOPLE ARE NORMALLY
GIVEN AWAY
three or more.
EACH BENEFIT IS SAMPLED
INDEPENDENTLY
PRECISELY WHAT IS MEAN SQ . WITHIN?
Mean
square Within is the value
that approximate the population
variances of each
group( considering that the
groups will be homogenous as stated
in the supposition.
Formula:
WHAT IS INDICATE SQUARE
AMONG?
MEAN
SQ . BETWEEN CAN BE AN
ESTIMATOR OF THE INHABITANTS
VARIANCE IN CASE THE PPULATION
MEANS ARE EQUAL. IF THE MEANS
ARE NOT EQUIVALENT IT ESTIMATIONS A
BIGGER QUANTITY.
Formula:
= / (n-1)
FACTORS AND LEVELS
FACTOR
– A ATTRIBUTE
UNDER CONSIDERATION, BELIEVED
TO INFLUENCE THE TESTED
OBSERVATIONS.
LEVEL
– A VALUE FROM THE FACTOR.
EINE WAY ( FACTOR) ANOVA
ON THE WHOLE ONE WAY ANOVA TECHNIQUES CAN BE USED TO
STUDY THE RESULT OF E (> 2) LEVELS OF A SINGLE FACTOR
EXAMPLE:
THE TABLE SHOWS THE LIFETIMES UNDERNEATH CONTROLLED
CIRCUMSTANCES, IN HOURS IN EXCSS OF a thousand HRS, OF SAMPLES OF
60w ELECTRIC LIGHT BULBS OF THREE DIFFERENT BRAND
BRAND
one particular
2
three or more
16
18
26
12-15
22
thirty-one
13
twenty
24
21
16
30
14
twenty-four
24
SUMMARIZE DATA
COMPANY
1
2
3
SAMPLE SIZE
your five
5
a few
SUM
85
100
one hundred thirty five
SUM OF
SQUARES
1316
2040
3689
MEAN
sixteen
20
twenty-seven
VARIANCE
9
10
10
SINCE EACH OF THESE THREE SAMPLE VARIANCES IS AN
ESTIMATION OF THECOMMON POPULATION VARIANCE. A POOLED
ESTIMATE CAN BE CALCULATED INSIDE THE USUAL WAY.
= 10
THE VARIABILITY BETWEEN SAMPLES CAN BE COMPUTED BY TE
3 SAMPLE MEANS
BRAND
MPLE MEAN
you
2
a few
16
20
27
SUM
63
TOTAL OF
SQUARES
1385
INDICATE
21
VARIANCE
31
THIS
DIFFERENCE, DENOTED SIMPLY BY IS CALLED DIFFERENCE BETWEEN
TEST MEANS BASED UPON (3-1) a couple of DEGREES OF LIBERTY,
BUT ONLY WHEN THE NULL IS HOLDS TRUE, IF THE NULL IS PHONY,
THEN THE FUTURE " SIGNIFICANT DFFERENCES AMONG
SAMPLE MEANS WILL BE SEEN.
ANOTHER WAY OF SOLVING
ANOVA
COMPUTATIONAL FORMULA
TOTAL SUM OF PIECES SSt – total coming from all squared info
Among sample amount of potager SSb = the quantity of square-shaped total per column divided by d – rectangular of summation of all data over in
SSw = SSt – SSb
MSt = SSt / n-1; MSb sama dengan SSb as well as (k-1); MSw = SSw / and - k
Anova computation (II)
=
1316
+2040 +3689 - = 7845 – 6615 = 430
-- 6615 = 1280+2000+3645 – 6615 = 6925 – 6615 = 310
MSb = 310 / two = 155
MSw sama dengan 120 /12 = 12
F = 155/10 = 15. 5
EXAMPLE a couple of
WITHIN A COMPARISON OF THE CLENING ACTION OF 4
DETERGENTS, twenty PIECES OF WHITE CLOTH HAD BEEN
FIRST DIRTY WITH INDIA INK. THE CLOTHS
HAD BEEN THEN CLEANED UNDER CONTROLLED
CONDITIONS WITH 5 PARTS EACH LAUNDERED BY
EACH OF THE DETERGENTS. UNFORTUNATELY
THREE PIECES OF CLOTH WERE LOST IN
THECOURSE OF EXPERIMENTATION. WHITENESS
READING MANUFACTURED ON THE 17 REMAINING BITS
OF CLOTH HAPPEN TO BE SHOWN:
DETERGENT
A
N
C
M
77
seventy four
73
seventy six
81
66
78
85
61
58
57
seventy seven
76
69
64
69
63
ASSUMING MOST WHITENESS PSYCHIC READINGS TO BE NORMALLY
DISTRIBUTED WITH COMMON DIFFERENCE, TEST THE
HYPOTHESISOF SIMPLY NO DIFFERENCE BEETWEEN THE 4
BRANDS IN RELATION TO MEAN WHITENESS READINGS FOLLOWING
WASHING....
