Manuals/calci/Bartlett'sTest

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 BCriticl 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	7.810299999999978
RESULT	THE P-VALUE IS LESSER THAN THE B-CRITICAL VALUE, SO THE VARIANCES ARE JUDGED TO BE EQUAL.

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