{"id":43571,"date":"2014-07-14T16:04:42","date_gmt":"2014-07-14T10:34:42","guid":{"rendered":"http:\/\/www.vskills.in\/certification\/tutorial\/?p=43571"},"modified":"2024-04-12T14:19:51","modified_gmt":"2024-04-12T08:49:51","slug":"hypothesis-testing","status":"publish","type":"page","link":"https:\/\/www.vskills.in\/certification\/tutorial\/hypothesis-testing\/","title":{"rendered":"Hypothesis Testing"},"content":{"rendered":"\n
\"Hypothesis<\/a><\/figure><\/div>\n\n\n

Hypothesis Testing-<\/strong> A hypothesis<\/strong> is a theory about the relationships between variables. Statistical analysis is used to determine if the observed differences between two or more samples are due to random chance or to true differences in the samples.<\/p>\n

\"hypothesis\"<\/a><\/p>\n

Basics<\/strong><\/h5>\n

Hypothesis Testing- A hypothesis is a value judgment, a statement based on an opinion about a population. It is developed to make an inference about that population. Based on experience, a design engineer can make a hypothesis about the performance or qualities of the products she is about to produce, but the validity of that hypothesis must be ascertained to confirm that the products are produced to the customer\u2019s specifications. A test must be conducted to determine if the empirical evidence does support the hypothesis.<\/strong><\/p>\n

Practical Significance<\/strong> – Practical significance is the amount of difference, change or improvement that will add practical, economic or technical value to an organization.<\/p>\n

Statistical Significance<\/strong> – Statistical significance is the magnitude of difference or change required to distinguish between a true difference, change or improvement and one that could have occurred by chance. The larger the sample size, the more likely the observed difference is close to the actual difference.<\/p>\n

Null<\/strong>– The first step consists in stating the hypothesis. It is denoted by H0,<\/strong> and is read \u201cH sub zero.\u201d The statement will be written as H0: \u00b5 = 20%. A null hypothesis assumes no difference exists between or among the parameters being tested and is often the opposite of what is hoped to be proven through the testing. The null hypothesis is typically represented by the symbol Ho.<\/strong><\/p>\n

\"Null<\/a><\/p>\n

Alternate Hypothesis<\/strong> – If the hypothesis is not rejected, exactly 20 percent of the defects will actually be traced to the CPU socket. But if enough evidence is statistically provided that the null hypothesis is untrue, an alternate hypothesis should be assumed to be true. That alternate hypothesis, denoted H1,<\/strong> tells what should be concluded if H0 is rejected. H1 : \u00b5 \u2260 20%. An alternate hypothesis assumes that at least one difference exists between or among the parameters being tested. This hypothesis is typically represented by the symbol Ha.<\/strong><\/p>\n

Test Statistic<\/strong> – The decision made on whether to reject H0<\/strong> or fail to reject it depends on the information provided by the sample taken from the population being studied. The objective here is to generate a single number that will be compared to H0<\/strong> for rejection. That number is called the test statistic.<\/strong><\/p>\n

The level of risk<\/strong> – It addresses the risk of failing to reject a hypothesis when it is actually false, or rejecting a hypothesis when it is actually true.<\/p>\n

Type I error (False Positive)<\/strong> \u2013 It occurs when one rejects the null hypothesis when it is true. The probability of a type I error is the level of significance of the test of hypothesis, and is denoted by *alpha*.<\/strong> Usually a one-tailed test of hypothesis is used when one talks about type I error<\/strong> or alpha error<\/strong>.<\/p>\n

Type II error (False Negative)<\/strong> \u2013 It occurs when one rejects the alternative hypothesis (fails to reject the null hypothesis) when the alternative hypothesis is true. The probability of a type II error<\/strong> is denoted by *beta*.<\/strong><\/p>\n

Decision Rule Determination<\/strong> – The decision rule determines the conditions under which the null hypothesis is rejected or not. The critical value is the dividing point between the area where H0<\/strong> is rejected and the area where it is assumed to be true.<\/p>\n

Decision Making<\/strong> – Only two decisions are considered, either the null hypothesis is rejected or it is not. The decision to reject a null hypothesis or not depends on the level of significance. This level often varies between 0.01 and 0.10. Even when we fail to reject the null hypothesis, we never say \u201cwe accept the null hypothesis\u201d because failing to reject the null hypothesis that was assumed true does not equate proving its validity.<\/p>\n

Testing for a Population Mean<\/strong> – When the sample size is greater than 30 and \u03c3 is known, the Z formula can be used to test a null hypothesis about the mean.<\/p>\n

Phrasing<\/strong> – In hypothesis, the phrase \u201cto accept\u201d the null hypothesis is not typically used. In statistical terms, the Six Sigma Black Belt can reject the null hypothesis, thus accepting the alternate hypothesis, or fail to reject the null hypothesis. This phrasing is similar to jury’s stating that the defendant is not guilty, not that the defendant is innocent.<\/p>\n

One Tail Test<\/strong> – In a one-tailed t-test, all the area associated with a is placed in either one tail or the other. Selection of the tail depends upon which direction to bs would be (+ or -) if the results of the experiment came out as expected. The selection of the tail must be made before the experiment is conducted and analyzed.<\/p>\n

Sample Size<\/strong> – It has been assumed that the sample size (n<\/strong>) for hypothesis testing has been given and that the critical value of the test statistic will be determined based on the error that can be tolerated.<\/p>\n

Paired-Comparison Tests<\/strong>
They are powerful ways to compare data sets by determining if the means of the paired samples are equal. Making both measurements on each unit in a sample allows testing on the paired differences. An example of a paired comparison is two different types of hardness tests conducted on the same sample.<\/p>\n

Once paired, a test of significance attempts to determine if the observed difference indicates whether the characteristics of the two groups are the same or different. A paired comparison experiment is an effective way to reduce the natural variability that exists among subjects and tests the null hypothesis that the average of the differences between a series of paired observations is zero.<\/p>\n

Goodness of Fit<\/strong> – GOF (Goodness of Fit) tests are part of a class of procedures that are structured in cells. In each cell there is an observed frequency. In the goodness-of-fit tests, one is comparing and observed (O)<\/strong> frequency distribution to an expected (E)<\/strong> frequency distribution. The relationship is statistically described by a hypothesis test<\/p>\n