Generalization of Klotz’s Test

Karaman, Filiz

doi:10.3923/jas.2009.2916.2924

Cited by 1 publication

(11 citation statements)

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“…For the fixed two‐way design with equal replication, as explained in Karaman's paper (Karaman ), the cell mean model is

y_{i j k} = {italicμ}_{i j} + {italicε}_{i j k}

, where

i = 1, \dots, t_{A} > 1

j = 1, \dots, t_{B} > 1

, k =1,…, n >1. In the model,

y_{i j k}

denotes the k th response from the i th level of factor A and the j th level of factor B .…”

Section: Model and Hypothesesmentioning

confidence: 99%

“…Instead of using the usual one‐way ANOVA analysis to test for equality of variance, following the studies of Ozaydin et al . () and Karaman (), an analysis that is analogous to the usual ANOVA for a two‐way replicated treatment structure is performed. The null hypotheses which are used to detect the form of the difference, are as follows:

H_{0} : {italicσ}_{11}^{2} - {italicσ}_{12}^{2} = {italicσ}_{21}^{2} - {italicσ}_{22}^{2}

.…”

Section: Model and Hypothesesmentioning

confidence: 99%

“…Following Conover et al . () and Karaman (), instead of using pseudo‐observations equal to deviations from the mean, variables

Z_{i j k} = false(y_{i j k} - {\bar{y}}_{i j .} false),

i = 1, \dots, t_{A}

j = 1, \dots, t_{B}

, k =1,…, n are constructed. The

Z_{i j k}

's are then ranked from the smallest to the largest (i.e.…”

Section: Test Procedures and Notationmentioning

confidence: 99%

“…The ranks are denoted by

R_{i j k}

. Following Karaman (), if there are ties in the sample, the average of the ranks of the tied values is calculated. Then the average is used as the

R_{i j k}

value for the tied

Z_{i j k}

's.…”

Section: Test Procedures and Notationmentioning

confidence: 99%

“…(). The generalisation of Klotz's test was considered by Karaman (). Elmore, Hettmansperger & Xuan () generalised Mood's median test for one‐way designs.…”

Section: Introductionmentioning

confidence: 99%

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Generalisation of Mood's Test to Factorial Designs to Detect Heterogeneity of Variances

Karaman

Çene

2015

Aus NZ J of Statistics

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Mood's test, which is a relatively old test (and the oldest non-parametric test among those tests in its class) for determining heterogeneity of variance, is still being widely used in different areas such as biometry, biostatistics and medicine. Although it is a popular test, it is not suitable for use on a two-way factorial design. In this paper, Mood's test is generalised to the 2 × 2 factorial design setting and its performance is compared with that of Klotz's test. The power and robustness of these tests are examined in detail by means of a simulation study with 10,000 replications. Based on the simulation results, the generalised Mood's and Klotz's tests can especially be recommended in settings in which the parent distribution is symmetric. As an example application we analyse data from a multi-factor agricultural system that involves chilli peppers, nematodes and yellow nutsedge. This example dataset suggests that the performance of the generalised Mood test is in agreement with that of the generalised Klotz's test.

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“…For the fixed two‐way design with equal replication, as explained in Karaman's paper (Karaman ), the cell mean model is

y_{i j k} = {italicμ}_{i j} + {italicε}_{i j k}

, where

i = 1, \dots, t_{A} > 1

j = 1, \dots, t_{B} > 1

, k =1,…, n >1. In the model,

y_{i j k}

denotes the k th response from the i th level of factor A and the j th level of factor B .…”

Section: Model and Hypothesesmentioning

confidence: 99%

H_{0} : {italicσ}_{11}^{2} - {italicσ}_{12}^{2} = {italicσ}_{21}^{2} - {italicσ}_{22}^{2}

.…”

Section: Model and Hypothesesmentioning

confidence: 99%

“…Following Conover et al . () and Karaman (), instead of using pseudo‐observations equal to deviations from the mean, variables

Z_{i j k} = false(y_{i j k} - {\bar{y}}_{i j .} false),

i = 1, \dots, t_{A}

j = 1, \dots, t_{B}

, k =1,…, n are constructed. The

Z_{i j k}

's are then ranked from the smallest to the largest (i.e.…”

Section: Test Procedures and Notationmentioning

confidence: 99%

“…The ranks are denoted by

R_{i j k}

. Following Karaman (), if there are ties in the sample, the average of the ranks of the tied values is calculated. Then the average is used as the

R_{i j k}

value for the tied

Z_{i j k}

's.…”

Section: Test Procedures and Notationmentioning

confidence: 99%

“…(). The generalisation of Klotz's test was considered by Karaman (). Elmore, Hettmansperger & Xuan () generalised Mood's median test for one‐way designs.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations