Table of Contents

* This study guide was updated on 31 Aug, 2009.

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SAMPLE TEXT on Design of Experiment

Design of Experiment (DoE) is a structured organized method for determining the relationship between the different factors (Xs) that can affect a process and the output of that process (Y). Implementation of DoE would involve designing a set of ten to twenty experiments, in which all relevant factors may vary systematically. When the results of these experiments are analyzed, one can identify the optimal conditions, the factors that most influence the results, and those that do not, plus other details such as the existence of interactions and synergies between different factors.

DoE methods require well-structured data matrices. When applied to a well-structured matrix, analysis of variance can deliver highly accurate results, even when the matrix being analyzed is small.


SAMPLE TEXT on Statistical Hypothesis

A hypothesis is a proposed explanation for an observable phenomenon. A working hypothesis is a provisionally accepted hypothesis. Generally speaking, a hypothesis cannot be confirmed as there is always a possibility that future experiment can disprove it. Hence, failing to falsify a hypothesis doesn't really prove that hypothesis. In other words, a conclusion would always remain provisional. Still, a hypothesis that has been rigorously tested and not falsified can form a reasonable basis for action.

When performing statistical hypothesis testing, you need to have two hypotheses compared. They are being referred to as the null hypothesis and the alternative hypothesis. The null hypothesis is the hypothesis stating that there is no relation between the phenomena whose relation is under investigation, or at least not of the form given by the alternative hypothesis. The alternative hypothesis is an alternative to the null hypothesis, which states that there is some sort of relation in existence. Proper use of statistical testing would require that these hypotheses and the threshold at which the null hypothesis is rejected and the alternative hypothesis is accepted.

A test statistic is a quantity calculated from a sample of data. Its value can be used for deciding whether or not the null hypothesis should be rejected. Do note that the choice of a test statistic would largely depend on the assumed probability model and the hypotheses under question.

SAMPLE TEXT on Critical Value, Rejection Region and Significance Level

The critical value(s) for a hypothesis test is a threshold to which the value of the test statistic in a sample is compared to determine whether or not the null hypothesis should be rejected. The critical value for any hypothesis test would really depend on the significance level at which the test is carried out, and whether the test should be made one-sided or two-sided.

NOTE: The sample space for the test statistic is partitioned into two regions, with one region (the critical region) leading us to reject the null hypothesis H0 and the other will not. The critical region CR (aka rejection region RR) is a set of values of the test statistic for which the null hypothesis should be rejected in a hypothesis test.

The rejection region is the part of the sample space (ie. critical region) where the null hypothesis H0 is rejected. The size of this region is usually determined by the probability (a) of the sample point falling in the critical region when H0 is true. a is being referred to as the level of significance, which is the probability of the value of the random variable falling in the critical region. The conclusion is that if the test statistic falls in the rejection/critical region, H0 is rejected, else H0 is accepted.

In a hypothesis test, a type I error can occur when the null hypothesis is wrongfully rejected. On the other hand, a type II error can occur when the null hypothesis is wrongfully accepted.