II. B. 3. Hypothesis Testing (parametric and non-parametric)

Hartley’s Test for Variance Homogeneity

The Hartley test is an extension of the F distribution based hypothesis test checking if two samples have different variances.

The F test works with two samples allowing us to compare two population variances based on the two samples. This test does not work for 3 or more populations. We could conduct multiple pairwise comparisons, yet the probability of an erroneous result is significant.

Bartlett’s Test and Levene’s Test are non-parametric checks for homogeneity of variances. Bartlett’s Test pretty much expects the underlying data to be normally distributed.

Levene’s Test is a better choice when you’re not sure the data is normal. Both are conservative and time-consuming to calculate.

We need another way to check for equal variances. [Read more…]

by Fred Schenkelberg 9 Comments

Bartlett’s Test for Homogeneity of Variances

A common assumption when comparing three or more normal population means is they have similar (the same) population variances.

ANOVA and some DOE analysis results rely on the underlying data having similar variances. If this assumption is not true, the conclusions suggested by the ANOVA or DOE may be misleading.

It doesn’t take long to check. [Read more…]

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Two Proportions Hypothesis Testing

In the article, Hypothesis Tests for Proportion, the comparison is between a given value and the sample. In this case, let’s compare two populations. We take a sample which provides a proportion representing each population and determines if the populations are different from each other based on the two samples.

The exact solution uses the Binomial distribution, yet when np and 1 – np are greater than 5, then we can use a normal approximation for the test statistic and critical value. [Read more…]

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Run Test for Randomness

It seems that anytime we draw a sample, it should be taken randomly. Statistics books and papers regularly advise using a random sample. The adverse effect on results drawn from the experiment may hinge on the randomness of the selection of samples. [Read more…]

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Mood’s Median Test

This nonparametric hypothesis test tests the equality of population medians. While not as powerful as the Kruskal-Wallis Test, it is useful for smaller sample sizes, when there are a few outliers or errors in the data as it focuses only on the median value. [Read more…]

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Kendall Coefficient of Concordance

Comparisons for agreement

Let’s say we have data that is only rank order from two or more evaluators (people, algorithms, etc.) and we want to determine if the evaluators agree or not.

The agreement here meaning the results from one person or another are in agreement, or they are concordant. This is typically done with this non-parametric method for 3 or more evaluators. For a comparison of two evaluators consider using Cohen’s Kappa or Spearman’s correlation coefficient as they are more appropriate. [Read more…]

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Hypothesis Test Selection Flowchart

This might be easier to read printed out.

[Read more…]

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Hypothesis Test Selection

Over the past few weeks, we have explored about 8 different hypothesis test formulas. There are more. So, how do you determine which test to perform? Well, that depends on the question you are trying to answer and the type of data you’re dealing with. [Read more…]

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The Paired-Comparison Hypotheses Test for Variances

The F-test provides a means to compare paired data variances. It is a variance hypothesis test.

If we are exploring the precision of one measuring device or another, or we are comparing assembly processes, we often want to know if the variance is different or not.
Working with data from normal distributions from two different processes or devices, we know from statistical theory that the ratio (s1)2 / (s2)2 is described by the F distribution.
There are three hypothesis test possible, basically to test if the population variances are different, or one is less than or greater than the other. The following details the three test’s null and alternative hypotheses. [Read more…]

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Hypothesis Tests for Variance Case II

The chi-square (Χ²) test provides the basis for the second case of hypothesis tests for variances. In this case, we want to compare observed and expected frequencies, or counts, of outcomes when there is no defined variance. In other words, we are working with attribute data. [Read more…]

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Hypothesis Un-Equal Variance

Hypothesis testing of data may include two populations that have un-equal standard deviations. The t-test for differences considered in a previous post used the assumption of equal variances to pool the variance value. In this test, we want to consider if one population is different in some way than the other and we use the samples from each population directly even if the population have difference variances. [Read more…]

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Equal Variance Hypothesis

Hypothesis testing of paired data may include two populations that have the equal standard deviations. The t-test for differences considered in a previous post used the standard deviation of the differences. In this test, we want to consider if one population is different in some way than the other and we use the samples from each population directly. [Read more…]

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Paired-Comparison Hypothesis Tests

Hypothesis testing previously discussed (link to past posts) generally considered samples from two populations. Maybe the experiments explored design changes, different component vendors, or two groups of customers. Occasionally you may find data that has some relationship between the samples, or where the samples are from the same population. Paired (or matched) data involves samples that are related in some meaningful way. [Read more…]

by Fred Schenkelberg 1 Comment

Hypothesis Tests for Variance Case I

Statistics is the language of variation. Everything varies, and we use variance (σ²) to describe the spread of the data. For any experimental work aimed at making improvements, whether in the design, manufacturing process or field performance, there are two ways to make improvements. Move the center of the distribution, or reduce the spread of the data. [Read more…]

by Fred Schenkelberg 3 Comments

Hypothesis Tests for Proportion

This is also called the “p test”

When comparing proportions that are from a population with a fixed number of independent trials and each trial has a constant probability of one or another outcome (Bernoulli experiments) then we can use a p test. p is the probability of success, and 1-p is the probability of failure. Caution: stay consistent once you define success otherwise, like me, you’ll have a bit of confusion. n is the number of trials. [Read more…]