Small Sample Power Research Articles

A Robust Test for Dispersion

Abstract The simplicity and surprisingly good small-sample power properties of the ordinary sign test motivate its use, in suitably adapted form, as a dispersion test. The proposed test statistic is based on the number of observations lying more than a specified distance from the sample mean. For symmetric and moderately skewed distributions, the proposed test is robust and has good power properties.

A Note on the Small-Sample Power Functions for Nonparametric Tests of Location in the Double Exponential Family

Abstract Eight nonparametric tests are examined in a small-sample setting. Their power functions are compared with the locally most powerful (LMP) linear rank test, primarily to see over which range the LMP test retains good power. All tests are two-sample tests, the populations are governed by the double exponential distribution, and the sample sizes are m = 5, n = 5, and m = 5, n = 4. The LMP test performs uniformly well, even under nonlocal alternatives, while its asymptotically equivalent counterpart, the median test, performs rather poorly with these small sample sizes.

A Note on the Small-Sample Power Functions for Nonparametric Tests of Location in the Double Exponential Family

A Note on the Small-Sample Power Functions for Nonparametric Tests of Location in the Double Exponential Family

Small Sample Distribution and Power of the Binomial Index of Dispersion and Log Likelihood Ratio Tests

AbstractThis paper considers the exact distribution of the X2 index of dispersion and ‐2 log (likelihood ratio) tests for the hypothesis of homogeneity of c independent samples from a common binomial population. The exact significance levels and power of these tests under ‘logit’ alternatives are compared numerically for the cases: c = 3, 4, 5 and various sample sizes. n1 = 5,10 for i = 1,…, c.

The power of the exponential scores test for an ordinary renewal process against trend alternatives

The power properties of a statistic based on the use of exponential scores which may be used for testing whether a series of events occurring in time form an ordinary renewal process against trend alternatives are examined. Small sample power comparisons under a Lehmann trend alternative are made with an alternative nonparametric test based on a rank trend statistic and with the parametric test when the intervals are exponentially distributed. Finally, some asymptotic efficiency results are developed for limiting trend alternatives.

U-statistics for skewness or symmetry

We propose certain U-statistics as intuitively reasonable measures of skewness and as criteria for asymptotically distribution-free tests of symmetry. Some comparisons are made with the moment-skewness b1 in terms of small-sample power and asymptotic relative efficiency.

Corrigenda: Small Sample Power Functions for Nonparametric Tests of Location in the Double Exponential Family

Corrigenda: Small Sample Power Functions for Nonparametric Tests of Location in the Double Exponential Family

Properties of the Exponential Scores Test for the K-Sample Problem Under the Lehmann Model

Summary Properties of an exponential scores statistic which provides a non-parametric test of the homogeneity of k continuous populations are considered. Tables of exact critical values are given for the case k = 3 and some small sample sizes and approximations to the critical values are developed and evaluated. Small sample power comparisons are made with the Kruskal–Wallis rank test under the Lehmann model and some asymptotic efficiency results are developed under a limiting form of this model. Finally, a modified form of the test to allow for censoring is presented.

A Cramér–Von Mises Type Goodness of Fit Statistic Related to √B 1 and B 2

Summary We investigate a statistic introduced by de Wet and Venter to test for normality and a Cramér–von Mises statistic asymptotically equivalent to this statistic. It is shown that the Cramér–von Mises statistic can be written as a sum of components which are polynomial functions of the original standardized observations, the most important of which are Pearson's moment ratio statistics, √b 1 and b 2. Approximate small sample percentage points are given for the de Wet and Venter statistic. The asymptotic power of this statistic is investigated and the results of a small sample power study reported, confirming these results.

Distribution-Free Two-Sample Tests for Scale

Abstract Several linear rank statistics have been proposed in the literature for the two-sample scale problem. We propose a new class of statistics which are distribution free when the populations are identical, but are not linear rank statistics. Our analogs of the Ansari-Bradley, Mood, and Klotz tests are of particular interest. Each has the same Pitman efficiency as its corresponding linear rank statistic, and yet our small-sample power is significantly higher. In addition, our tests are consistent for scale differences with unequal location in the case when the populations are symmetric and the sample sizes are equal.

Distribution-Free Two-Sample Tests for Scale

Abstract Several linear rank statistics have been proposed in the literature for the two-sample scale problem. We propose a new class of statistics which are distribution free when the populations are identical, but are not linear rank statistics. Our analogs of the Ansari-Bradley, Mood, and Klotz tests are of particular interest. Each has the same Pitman efficiency as its corresponding linear rank statistic, and yet our small-sample power is significantly higher. In addition, our tests are consistent for scale differences with unequal location in the case when the populations are symmetric and the sample sizes are equal.

Comment on the Small-Sample Power of Durbin'sh-Test

Abstract The power of Durbin's h-test for autocorrelated error terms is compared with the power of the Durbin-Watson d-test. It is argued that, contrary to conclusions reached elsewhere (see [6]), the d-test outperforms the h-test.

On the Small-Sample Power of Durbin'shTest

Abstract Durbin's h test for autocorrelated error terms is examined with respect to its small-sample power in addition to Durbin's other asymptotic test, the t test, and the Durbin-Watson bounds test. Using sampling experiments for regression with lagged values of the dependent variable with first-order autocorrelated disturbances, we find that both the h and t tests significantly outperform the Durbin-Watson bounds test and are acceptably powerful in small samples.

On the Small-Sample Power of Durbin's h Test

On the Small-Sample Power of Durbin's h Test

On the small sample distribution and power of the log likelihood ratio and variance tests for the poisson

The variance test and log likelihood ratio test are both well known in examining a series of n discrete observations for agreement with an assumed common Poisson distribution. This paper compares the tests in small samples with the corresponding x 2 significance levels, and also the small sample power under several Poisson-type alternatives.

Comparison of the Small Sample Power of the Chi-Square and Likelihood Ratio Tests of the Assumptions for Stochastic Models

Comparison of the Small Sample Power of the Chi-Square and Likelihood Ratio Tests of the Assumptions for Stochastic Models

Comparison of the Small Sample Power of the Chi-Square and Likelihood Ratio Tests of the Assumptions for Stochastic Models

Abstract When applying the Markov model, it is often assumed the transition matrix is stationary and of order one. This article considers the problem of applying the transformed likelihood ratio statistic and the contingency statistic to testing the assumptions of a particular order and of stationarity when the assumptions are not true. A Monte Carlo study of the small sample power of both these test statistics shows that if the true alpha level is kept equal for the two tests they have similar power. However, if the alpha level is set by reference to any standard table of the chi-square distribution the likelihood ratio statistic has larger power.

Small Sample Power of Some Tests of the Constant Failure Rate

The exponential distribution is often used in reliability work to describe the distribution of time to “chance” failure and is characterized by a constant failure rate. In this paper the small sample powers are compared for four test statistics for the hypothesis of constant failure rate vs. the hypothesis of non-constant failure rate. The tests are compared for samples of size n = 10(5)50 using the Weibull distribution for the alternative distribution. The shape parameter of the Weibull is varied from 0.5 to 2.5. For the two test statistics which involve arbitrary grouping of the data the effect of group size and number was also examined.

Small Sample Power of Some Tests of the Constant Failure Rate

The exponential distribution is often used in reliability work to describe the distribution of time to “chance” failure and is characterized by a constant failure rate. In this paper the small sample powers are compared for four test statistics for the hypothesis of constant failure rate vs. the hypothesis of non-constant failure rate. The tests are compared for samples of size n = 10(5)50 using the Weibull distribution for the alternative distribution. The shape parameter of the Weibull is varied from 0.5 to 2.5. For the two test statistics which involve arbitrary grouping of the data the effect of group size and number was also examined.

AN EMPIRICAL INVESTIGATION OF THE PERMUTATION t‐TEST

The small sample power and the probability of a Type I error of a permutation test were investigated for the two‐sample problem. Empirical probabilities were obtained under the null and various alternative conditions for the permutation t‐test and, for comparison, Student's t‐test and the Mann‐Whitney 17‐test for normal, uniform and skewed populations. Values of the empirical α were within sampling variation bounds of the theoretical α, and the power values for the permutation t‐test were generally close to those of Student's t‐test and the theoretical values. For the skewed population, the power values of the permutation t‐test were higher than those of Student's t‐test if the means were positively related to the sample sizes.