Parietal Numerics

Dispersion Tests

Chi-Square Test for Variance

Sign Test

Description

Determines if the variance of a population is equal to a specified value.

TailAlt. Hypothesis
leftleft\hspace{1cm}H1:σ2<σ02 H_{1}: \sigma^{2} \lt \sigma_{0}^{2}
rightright\hspace{1cm}H1:σ2>σ02 H_{1}: \sigma^{2} \gt \sigma_{0}^{2}
bothboth\hspace{1cm}H1:σ2≠σ02 H_{1}: \sigma^{2} \neq \sigma_{0}^{2}
Returns
  • p-value
  • decision
  • Chi-Sq statistic

F-Test for Two Variances

Two Sample F Test

Description

Determines if the variances of two populations are equal.

TailAlt. Hypothesis
leftleft\hspace{1cm}H1:σ12<σ22 H_{1}: \sigma_{1}^{2} \lt \sigma_{2}^{2}
rightright\hspace{1cm}H1:σ12>σ22 H_{1}: \sigma_{1}^{2} \gt \sigma_{2}^{2}
bothboth\hspace{1cm}H1:σ12≠σ22 H_{1}: \sigma_{1}^{2} \neq \sigma_{2}^{2}
Returns
  • p-value
  • decision
  • F statistic

Levene Test for Equal Variances

Levene’s Test

Description

Null hypothesis is that the population variances are equal.

The Levene test statistic is defined as: W=(N−k)(k−1)∑i=1kNi(Zˉi.−Zˉ..)2∑i=1k∑j=1Ni(Zij−Zˉi.)2 W = \frac{(N-k)} {(k-1)} \frac{\sum_{i=1}^{k}N_{i}(\bar{Z}_{i.}-\bar{Z}_{..})^{2} } {\sum_{i=1}^{k}\sum_{j=1}^{N_i}(Z_{ij}-\bar{Z}_{i.})^{2} }

where Zij=∣Yij−Yˉi.∣ Z_{ij} = |Y_{ij} - \bar{Y}_{i.}| and Yˉi. \bar{Y}_{i.} is the mean of the ith subgroup.

Returns
  • p-value
  • decision
  • F statistic
  • degrees of freedom
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