Difference between revisions of "Bartlett'sTest"

Latest revision as of 07:31, 19 August 2020

BARTLETTSTEST(DataRange, ConfidenceLevel, NewTableFlag)

$DataRange$ is the array of x values.
$ConfidenceLevel$ is the value from 0 to 1.
$NewTableFlag$ is either TRUE or FALSE. TRUE for getting results in a new cube. FALSE will display results in the same cube.

DESCRIPTION
Bartlett's test is used to test if k samples are from populations with equal variances.

Bartlett's test is sensitive to departures from normality.

That is, if the samples come from non-normal distributions, then Bartlett's test may simply be testing for non-normality.
$B={\frac {df_{W}lnMS_{W}-\sum _{j}df_{j}lns_{j}^{2}}{1+{\frac {1}{3(k-1)}}(\sum _{j}{\frac {1}{df_{j}}}-{\frac {1}{df_{W}}})}}$
B is the Bartlett's test static.

$MS_{W}$ is the pooled variance across all groups.

RESULT
If p-value is greater than BCritical value, reject the null hypothesis.

Else, retain null hypothesis.

EXAMPLE
Spreadsheet
A B C D

1 51 82 79 85

2 87 91 84 80

3 50 92 74 65

4 48 80 98 71

5 79 52 63 67

6 61 79 83 51

7 53 73 85 63

8 54 74 58 93

=BARTLETTSTEST([A1:A8, B1:B8, C1:C8, D1:D8], 0.05, true)

BARTLETT'S TEST
DATA-0 DATA-1 DATA-2 DATA-3

MEAN 60.375 77.875 78 71.875

VARIANCE 214.26785714285714 157.55357142857142 164.57142857142858 181.55357142857142

LNVARIANCE 5.367226901229239 5.059765536486956 5.1033446922005234 5.201550769540011

COUNT 8 8 8 8

DF 7 7 7 7

1/DF 0.14285714285714285 0.14285714285714285 0.14285714285714285 0.14285714285714285
ERROR
SAMPLE DATA

DF 28

1/DF 0.03571428571428571

VARIANCE 179.48660714285714

LNVARIANCE 5.19010059312721
RESULTS
DATA

B-NUMERATOR 0.19960131136474502

B-DENOMINATOR 1.0595238095238095

B 0.18838775454650092

P-VALUE 0.979441777737987

B-CRITICAL 7.814684159999997

RESULT THE P-VALUE IS LESSER THAN THE B-CRITICAL VALUE, SO THE VARIANCES ARE JUDGED TO BE EQUAL.

Comparison with other software

Bartlett's test to determine whether the 4 samples have significantly different population variances.

SOLUTION
In z3:

In R:

In Online Software:

z3 and the online software give the same P-value i.e 0.979.

R has a P-value of 0.9768.

@@ Line 1: / Line 1: @@
-<div style="font-size:25px">'''BARTLETTSTEST(DataRange,ConfidenceLevel,NewTableFlag)'''</div><br/>
+<div style="font-size:25px">'''BARTLETTSTEST(DataRange, ConfidenceLevel, NewTableFlag)'''</div>
-*<math>DataRange</math> is the array of x values.
+*'''<math>DataRange</math> is the array of x values.
-*<math>ConfidenceLevel</math> is the value from 0 to 1.
+*'''<math>ConfidenceLevel</math> is the value from 0 to 1.
-*<math>NewTableFlag</math> is either TRUE or FALSE. TRUE for getting results in a new cube. FALSE will display results in the same cube.
+*'''<math>NewTableFlag</math> is either TRUE or FALSE. TRUE for getting results in a new cube. FALSE will display results in the same cube.<br></br>
-==Description==
+==='''DESCRIPTION===
-* Bartlett's test is used to test if k samples are from populations with equal variances.
+* '''Bartlett's test is used to test if k samples are from populations with equal variances.
-* Bartlett's test is sensitive to departures from normality.
+* '''Bartlett's test is sensitive to departures from normality.
-* That is, if the samples come from non-normal distributions, then Bartlett's test may simply be testing for non-normality.
+* '''That is, if the samples come from non-normal distributions, then Bartlett's test may simply be testing for non-normality.
    <math>B=\frac{df_WlnMS_W-\sum_{j}df_jln s_j^2}{1+\frac{1}{3(k-1)}(\sum_{j}\frac{1}{df_j}-\frac{1}{df_W})}</math>
-* B is the Bartlett's test static.
+* '''B is the Bartlett's test static.
-* <math>MS_W</math> is the pooled variance across all groups.
+* '''<math>MS_W</math> is the pooled variance across all groups.<br></br>
-==Result==
+==='''RESULT===
-* If p-value is greater than BCritical value, reject the null hypothesis.
+* '''If p-value is greater than BCritical value, reject the null hypothesis.
-* Else retain null hypothesis.
+* '''Else, retain null hypothesis.<br></br>
-==Example==
+==='''EXAMPLE===
 {| class="wikitable"
 |+Spreadsheet
@@ Line 46: / Line 46: @@
 |54 || 74 || 58 || 93
 |}
-=BARTLETTSTEST([A1:A8,B1:B8,C1:C8,D1:D8],0.05,true)
+='''BARTLETTSTEST([A1:A8, B1:B8, C1:C8, D1:D8], 0.05, true)<br></br>
 {| class="wikitable"
 |+BARTLETT'S TEST
@@ Line 90: / Line 91: @@
 |P-VALUE || 0.979441777737987
 |-
-|B-CRITICAL || 7.810299999999978
+|B-CRITICAL || 7.814684159999997
 |-
 |RESULT || THE P-VALUE IS LESSER THAN THE B-CRITICAL VALUE, SO THE VARIANCES ARE JUDGED TO BE EQUAL.
 |}
+<br></br>
+===Comparison with other software===
+'''Bartlett's test to determine whether the 4 samples have significantly different population variances.<br><br>
+[[File:bart1.JPG]]<br><br>
+'''SOLUTION'''<br>
+'''In z3:'''<br>
+[[File:bartz.JPG]]<br><br>
+'''In R:'''<br>
+[[File:bartr.JPG]]<br><br>
+'''In Online Software:'''<br>
+[[File:bartos.JPG]]<br><br>
+'''In Online Software:'''<br>
+[[File:bartos2.JPG]]<br><br>
+* z3 and the online software give the same P-value i.e 0.979.
+* R has a P-value of 0.9768.

	A	B	C	D
1	51	82	79	85
2	87	91	84	80
3	50	92	74	65
4	48	80	98	71
5	79	52	63	67
6	61	79	83	51
7	53	73	85	63
8	54	74	58	93

	DATA-0	DATA-1	DATA-2	DATA-3
MEAN	60.375	77.875	78	71.875
VARIANCE	214.26785714285714	157.55357142857142	164.57142857142858	181.55357142857142
LNVARIANCE	5.367226901229239	5.059765536486956	5.1033446922005234	5.201550769540011
COUNT	8	8	8	8
DF	7	7	7	7
1/DF	0.14285714285714285	0.14285714285714285	0.14285714285714285	0.14285714285714285

	SAMPLE DATA
DF	28
1/DF	0.03571428571428571
VARIANCE	179.48660714285714
LNVARIANCE	5.19010059312721

	DATA
B-NUMERATOR	0.19960131136474502
B-DENOMINATOR	1.0595238095238095
B	0.18838775454650092
P-VALUE	0.979441777737987
B-CRITICAL	7.814684159999997
RESULT	THE P-VALUE IS LESSER THAN THE B-CRITICAL VALUE, SO THE VARIANCES ARE JUDGED TO BE EQUAL.

	A	B	C	D
1	51	82	79	85
2	87	91	84	80
3	50	92	74	65
4	48	80	98	71
5	79	52	63	67
6	61	79	83	51
7	53	73	85	63
8	54	74	58	93

	A	B	C	D
1	51	82	79	85
2	87	91	84	80
3	50	92	74	65
4	48	80	98	71
5	79	52	63	67
6	61	79	83	51
7	53	73	85	63
8	54	74	58	93