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Significance Tests / Hypothesis Testing

The z-score values of +1.96 are the critical values for a twotailed hypothesis test when using the normal distribution to representthe sample distribution.

Here is the recipe for all null hypothesis tests we’re going to see:

In this case, we would say we’ve performed a one-sided test, because we determined in advance that only values greater than 0.5 would cause us to reject the null hypothesis.

1. Specify H0 and HA – the null and alternative hypotheses

If the -value for the test is less than , we reject the null hypothesis.

The alternative hypothesis is the contrary of the null hypothesis, and so describes the cases where there is a difference among groups or a correlation between two variables, etc.

This statistical hypothesis holds a special place, and it is known as the null hypothesis. We’re going to focus a lot on the null hypothesis, and it’s a little strange, to be honest: the null hypothesis in this context is exactly the opposite of what we care about. It means that there’s nothing going on in the data, that our measurements weren’t that useful.

Treat each hypothesis as a two-tailed test with a .05 Type I error.

If the -value is greater than or equal to , we fail to reject the null hypothesis.

The answer is , we like a method to determine the likelihood of our hypothesis being true given our data, but we use the approach since it is relatively straightforward, and has wide acceptance historically and across fields.

Technically, the -value says nothing about the alternative hypothesis. But logically, if the null hypothesis is rejected, then its logical complement, the alternative hypothesis, is supported. Practically, this is how we handle significant -values, though this practical approach generates disapproval in some theoretical circles.

The test I just performed on all y’alls data was a test of the following hypotheses:
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1. Which of the following pair is the null hypothesis?

(Hint: You should reject the null hypothesis when the percentage inthe box in the center of the distribution is less than 2.5%.)The above exercise is very similar to how a researcher uses anindependent samples t-test.

2. Which of the following pair is the null hypothesis?

Particularly in the fields of psychology and education, there has been much criticism of the null hypothesis significance test approach. From my reading, the main complaints against NHST tend to be:

3. Which of the following pair is the null hypothesis?

Further, the standard deviation (i.e., the standard error) of thesampling distribution of the difference between the means must beestimated because the decision to reject the null hypothesis is basedon how many standard error units the observed difference in the samplemeans is from zero.

Null and Alternative Hypothesis | Real Statistics Using …

The null hypothesis predicts that two groups who differ on theindependent variable can nonetheless be treated as the same populationwhen it comes to the variable of interest (in our example, thevariable of interest is satisfaction with dorm living).

Hypothesis Testing | R Tutorial

The alternative hypothesis states that the two samples come from differentpopulations for the variable of interest and can be stated as1 - 2 is not equal to zero(for the two-tailed test) or 1- 2 is greater than zero(for the one-tailed test) or 1- 2 is less than zero (for the one-tailed test in the other direction).

Rejecting the null hypothesis means that the null ..

For these comparisons, the null hypothesis is that the two samples canbe treated as members of the same population for the variable of interest(e.g., satisfaction with dorm living).

Hypothesis Testing - SlideShare

Instead, the researcher will usually enter the data into computer anduse statistical software that computes the observed t-value andprovides a probability of the observed t-value occurring assuming thenull hypothesis is true.

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