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How to Set Up a Hypothesis Test: Null versus Alternative
Here we presented hypothesis testing techniques for means and proportions in one and two sample situations. Tests of hypothesis involve several steps, including specifying the null and alternative or research hypothesis, selecting and computing an appropriate test statistic, setting up a decision rule and drawing a conclusion. There are many details to consider in hypothesis testing. The first is to determine the appropriate test. We discussed Z and t tests here for different applications. The appropriate test depends on the distribution of the outcome variable (continuous or dichotomous), the number of comparison groups (one, two) and whether the comparison groups are independent or dependent. The following table summarizes the different tests of hypothesis discussed here.
If our statistical analysis shows that the significance level is below the cut-off value we have set (e.g., either 0.05 or 0.01), we reject the null hypothesis and accept the alternative hypothesis. Alternatively, if the significance level is above the cut-off value, we fail to reject the null hypothesis and cannot accept the alternative hypothesis. You should note that you cannot accept the null hypothesis, but only find evidence against it.
All null hypotheses include an equal sign in them.
Now that you have identified the null and alternative hypotheses, you need to find evidence and develop a strategy for declaring your "support" for either the null or alternative hypothesis. We can do this using some statistical theory and some arbitrary cut-off points. Both these issues are dealt with next.
Scientists can really change the world with their hypotheses and findings. In an effort to improve the world we live in, all it takes is an initial hypothesis that is well-stated, founded in truth, and can withstand extensive research and experimentation. Seek out your independent and dependent variables and go on out here and make this world a better place. Good luck!
H0: Null hypothesis (no change, no difference);
The is the one you would believe if the null hypothesis is concluded to be untrue. The evidence in the trial is your data and the statistics that go along with it. All hypothesis tests ultimately use a -value to weigh the strength of the evidence (what the data are telling you about the population). The -value is a number between 0 and 1 and interpreted in the following way:
Not so long ago, people believed that the world was flat.
Null hypothesis, H0: The world is flat.
Alternate hypothesis: The world is round.
Several scientists, including , set out to disprove the null hypothesis. This eventually led to the rejection of the null and the acceptance of the alternate. Most people accepted it — the ones that didn’t created the !. What would have happened if Copernicus had not disproved the it and merely proved the alternate? No one would have listened to him. In order to change people’s thinking, he first had to prove that their thinking was wrong.
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Very few hypotheses can be stated without assumptions.
How likely is it to get this sample, or one with even asmaller sample proportion, if the null hypothesis H0 is true?The p-value is 0.000 020, so if there’s no racialbias in selection then there are only two chances in a hundredthousand of getting eight or fewer African Americans in a 100-manjury pool. (There’s a lot more aboutinterpreting the p-value .)
The null hypothesis usually is a statement
There is another surprising connection between hypothesistesting and our criminal justice system -- they were both British in origin!(remember the term "null" in ?) The modern theory of hypothesis testing was invented by aBritish statistician named , and to this day, the top journals in statistics are stillpublished in England (such as Biometrika and Journal of the Royal StatisticalSociety).
From the (word) problem, determine the appropriate null hypothesis,
The probability that the data could have occurred, if thenull hypothesis were true, is what we called the p-value (we'll go into p-valuein the next section in more detail), and we compare it to a quantity called (the same old , 1 minus the confidence level, that we encountered increating confidence intervals), which in this context is called the level ofsignificance, and represents the largest probability we’re willing to risk ofmaking a Type I error. We want to keep a tight lid on . We don’t want to make Type I errors! We would rather makeType II errors, if we have to make an error, and of course the more strictly welimit the likelihood of making Type I errors, the more probable it becomes thatwe’re making Type II errors. There is a rather intricate relationship betweenthe two errors: but there is a crucial difference from a practical point ofview: once the data has been collected, the likelihood of Type I error isentirely up to us! Just choose a small enough will ensure the Type Ierror is small. While to keep Type II error low, you will need more data. Youcan take entire course on these two types of errors, and some of the exercisesin our team homework are designed to give you some visual examples of what eachone represents.
Draw the conclusion: Reject or fail to reject the null hypothesis,
So here is my (completely unsubstantiated) theory of how theconvoluted language in hypothesis testing was invented: as a student, KarlPearson studied Roman Law. So naturally, he saw the parallel betweenstatistical decisions and criminal justice. Moreover, we know that the Britishpeople love to make sentences with multiple negatives! One need to look nofurther than the popular British TV Series: Downton Abbey . Coincidently, thestory line spanned the years from 1912 to 1921, which was the time Karl Pearsonestablished Hypothesis Testing (I would like to believe this one wasstatistically significant:)
Here, the null hypothesis is that the person is innocent, and the
You can think of a test statistic as a measure ofunbelievability, of disagreement between H0 and your sample. A sample hardly ever matches your null hypothesis perfectly, but thecloser the test statistic is to zero the better the agreement, and thefurther the test statistic is from 0 the worse the sample and the nullhypothesis disagree with each other.
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