When conducting any statistical test which hypothesis states there will be no significant results?
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7. Product and Process Comparisons
For more discussion about the meaning of a statistical hypothesis test, see Chapter 1. Show
The testing procedure works this way. Linewidths at random positions on the photomask are measured using a scanning electron microscope. A test statistic is computed from the data and tested against pre-determined upper and lower critical values. If the test statistic is greater than the upper critical value or less than the lower critical value, the null hypothesis is rejected because there is evidence that the mean linewidth is not 500 micrometers. One-sided tests of hypothesis Null and alternative hypotheses can also be one-sided. For example, to ensure that a lot of light bulbs has a mean lifetime of at least 500 hours, a testing program is implemented. The null hypothesis, in this case, is that the mean lifetime is greater than or equal to 500 hours. The complement or alternative hypothesis that is being guarded against is that the mean lifetime is less than 500 hours. The test statistic is compared with a lower critical value, and if it is less than this limit, the null hypothesis is rejected.Thus, a statistical test requires a pair of hypotheses; namely,
Further guidance on statistical hypothesis testing, significance levels and critical regions, is given in Chapter 1. A hypothesis that states that there is no relationship between two population parameters What is the Null Hypothesis?The null hypothesis states that there is no relationship between two population parameters, i.e., an independent variable and a dependent variable. If the hypothesis shows a relationship between the two parameters, the outcome could be due to an experimental or sampling error. However, if the null hypothesis returns false, there is a relationship in the measured phenomenon. The null hypothesis is useful because it can be tested to conclude whether or not there is a relationship between two measured phenomena. It can inform the user whether the results obtained are due to chance or manipulating a phenomenon. Testing a hypothesis sets the stage for rejecting or accepting a hypothesis within a certain confidence level. Two main approaches to statistical inference in a null hypothesis can be used– significance testing by Ronald Fisher and hypothesis testing by Jerzy Neyman and Egon Pearson. Fisher’s significance testing approach states that a null hypothesis is rejected if the measured data is significantly unlikely to have occurred (the null hypothesis is false). Therefore, the null hypothesis is rejected and replaced with an alternative hypothesis. If the observed outcome is consistent with the position held by the null hypothesis, the hypothesis is accepted. On the other hand, the hypothesis testing by Neyman and Pearson is compared to an alternative hypothesis to make a conclusion about the observed data. The two hypotheses are differentiated based on observed data. Summary
How the Null Hypothesis WorksA null hypothesis is a theory based on insufficient evidence that requires further testing to prove whether the observed data is true or false. For example, a null hypothesis statement can be “the rate of plant growth is not affected by sunlight.” It can be tested by measuring the growth of plants in the presence of sunlight and comparing this with the growth of plants in the absence of sunlight. Rejecting the null hypothesis sets the stage for further experimentation to see a relationship between the two variables exists. Rejecting a null hypothesis does not necessarily mean that the experiment did not produce the required results, but it sets the stage for further experimentation. To differentiate the null hypothesis from other forms of hypothesis, a null hypothesis is written as H0, while the alternate hypothesis is written as HA or H1. A significance test is used to establish confidence in a null hypothesis and determine whether the observed data is not due to chance or manipulation of data. Researchers test the hypothesis by examining a random sample of the plants being grown with or without sunlight. If the outcome demonstrates a statistically significant change in the observed change, the null hypothesis is rejected. Null Hypothesis ExampleThe annual return of ABC Limited bonds is assumed to be 7.5%. To test if the scenario is true or false, we take the null hypothesis to be “the mean annual return for ABC limited bond is not 7.5%.” To test the hypothesis, we first accept the null hypothesis. Any information that is against the stated null hypothesis is taken to be the alternative hypothesis for the purpose of testing the hypotheses. In such a case, the alternative hypothesis is “the mean annual return of ABC Limited is 7.5%.” We take samples of the annual returns of the bond for the last five years to calculate the sample mean for the previous five years. The result is then compared to the assumed annual return average of 7.5% to test the null hypothesis. The average annual returns for the five-year period are 7.5%; the null hypothesis is rejected. Consequently, the alternative hypothesis is accepted. What is an Alternative Hypothesis?An alternative hypothesis is the inverse of a null hypothesis. An alternative hypothesis and a null hypothesis are mutually exclusive, which means that only one of the two hypotheses can be true. A statistical significance exists between the two variables. If samples used to test the null hypothesis return false, it means that the alternate hypothesis is true, and there is statistical significance between the two variables. Purpose of Hypothesis TestingHypothesis testing is a statistical process of testing an assumption regarding a phenomenon or population parameter. It is a critical part of the scientific method, which is a systematic approach to assessing theories through observations and determining the probability that a stated statement is true or false. A good theory can make accurate predictions. For an analyst who makes predictions, hypothesis testing is a rigorous way of backing up his prediction with statistical analysis. It also helps determine sufficient statistical evidence that favors a certain hypothesis about the population parameter. Additional ResourcesThank you for reading CFI’s guide to Null Hypothesis. To keep advancing your career, the additional resources below will be useful:
Which hypothesis states that no statistical significance exists?The null hypothesis is a typical statistical theory which suggests that no statistical relationship and significance exists in a set of given single observed variable, between two sets of observed data and measured phenomena.
When can we say when the null hypothesis is significant or not?If there is less than a 5% chance of a result as extreme as the sample result if the null hypothesis were true, then the null hypothesis is rejected. When this happens, the result is said to be statistically significant .
When a statistical test is not significant this means?This means that the results are considered to be „statistically non-significant‟ if the analysis shows that differences as large as (or larger than) the observed difference would be expected to occur by chance more than one out of twenty times (p > 0.05).
What does the no hypothesis state?What is the Null Hypothesis? The null hypothesis states that there is no relationship between two population parameters, i.e., an independent variable and a dependent variable. If the hypothesis shows a relationship between the two parameters, the outcome could be due to an experimental or sampling error.
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