CRE Preparation Notes

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…]

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…]

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…]

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…]

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…]

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…]

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…]