How to Set Up a Hypothesis Test: Null versus Alternative

Accepting the does not mean that it is true. It is still a hypothesis, and must conform to the principle of , in the same way that rejecting the null does not prove the alternative.

One can never prove the truth of a statistical (null) hypothesis.

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rejecting the null hypothesis when the alternative is true.

Simple logistic regression finds the equation that best predicts the value of the Y variable for each value of the X variable. What makes logistic regression different from linear regression is that you do not measure the Y variable directly; it is instead the probability of obtaining a particular value of a nominal variable. For the spider example, the values of the nominal variable are "spiders present" and "spiders absent." The Y variable used in logistic regression would then be the probability of spiders being present on a beach. This probability could take values from 0 to 1. The limited range of this probability would present problems if used directly in a regression, so the odds, Y/(1-Y), is used instead. (If the probability of spiders on a beach is 0.25, the odds of having spiders are 0.25/(1-0.25)=1/3. In gambling terms, this would be expressed as "3 to 1 odds against having spiders on a beach.") Taking the natural log of the odds makes the variable more suitable for a regression, so the result of a logistic regression is an equation that looks like this:

not rejecting the null hypothesis when the alternative is true.

In the output above, Minitab reports that the P-value is 0.158. Since the P-value, 0.158, is greater than α = 0.05, the quality control specialist fails to reject the null hypothesis. There is insufficient evidence, at the α = 0.05 level, to conclude that the mean thickness of all pieces of spearmint gum differs from 7.5 one-hundredths of an inch.


Civil Essay: Simple Null Hypothesis Example free …

The major problem with the H0 is that many researchers, and reviewers, see accepting the null as a failure of the . This is very poor science, as accepting or rejecting any hypothesis is a positive result.

A Null Hypothesis for the New Year | Flirting with Models

If the biologist used the P-value approach to conduct her hypothesis test, she would determine the area under a t = t curve and to the left of the test statistic t* = -4.60:

Simple hypotheses only test against one value of the ..

In the output above, Minitab reports that the P-value is 0.000, which we take to mean P-value is less than 0.001, it is clearly less than α = 0.05, and the biologist rejects the null hypothesis. There is sufficient evidence, at the α = 0.05 level, to conclude that the mean height of all such sunflower seedlings is less than 15.7 cm.

What Are Examples of a Hypothesis

If the quality control specialist sets his significance level α at 0.05 and used the critical value approach to conduct his hypothesis test, he would reject the null hypothesis if his test statistic t* were less than -2.2622 or greater than 2.2622 (determined using statistical software or a t-table):

Simple Hypothesis and Composite Hypothesis | …

Later someone proposed an alternative hypothesis that the sun itself also circled around the something within the galaxy, thus creating a new H0. This is how research works - the H0 gets closer to the reality each time, even if it isn't correct, it is better than the last H0.

How to Set Up a Hypothesis Test: Null versus Alternative

Simple logistic regression assumes that the relationship between the natural log of the odds ratio and the measurement variable is linear. You might be able to fix this with a of your measurement variable, but if the relationship looks like a U or upside-down U, a transformation won't work. For example, Suzuki et al. (2006) found an increasing probability of spiders with increasing grain size, but I'm sure that if they looked at beaches with even larger sand (in other words, gravel), the probability of spiders would go back down. In that case you couldn't do simple logistic regression; you'd probably want to do with an equation including both X and X2 terms, instead.