## Significance Tests / Hypothesis Testing

The above states that the probability that an individual is in Group 1 and their outcome is Response Option 1 is computed by multiplying the probability that person is in Group 1 by the probability that a person is in Response Option 1. To conduct the χ^{2} test of independence, we need expected __frequencies__ and not expected __probabilities__. To convert the above probability to a frequency, we multiply by N. Consider the following small example.

Therefore, believing in aliens *is* a scientific hypothesis because it *can* be disproved (even though we haven't disproved it yet and might never manage to disprove it).

If Psychologists want to be scientific, as well as an alternative hypothesis, they will need to frame a .

## Null and Alternative Hypotheses for a Mean

On the other hand,we can see on the graph that the probability of getting, say 45 heads is still prettyhigh, and we might very well want to accept the null hypothesis in this case.

## Null hypothesis: μ = 72 Alternative hypothesis: μ ≠72

In this example, we have one sample and a discrete (ordinal) outcome variable (with three response options). We specifically want to compare the distribution of responses in the sample to the distribution reported the previous year (i.e., 60%, 25%, 15% reporting no, sporadic and regular exercise, respectively). We now run the test using the five-step approach.

## Let's look at an example using a 2-tailed hypothesis.

In the olden days, when people looked up *P* values in printed tables, they would report the results of a statistical test as "*P**P**P*>0.10", etc. Nowadays, almost all computer statistics programs give the exact *P* value resulting from a statistical test, such as *P*=0.029, and that's what you should report in your publications. You will conclude that the results are either significant or they're not significant; they either reject the null hypothesis (if *P* is below your pre-determined significance level) or don't reject the null hypothesis (if *P* is above your significance level). But other people will want to know if your results are "strongly" significant (*P* much less than 0.05), which will give them more confidence in your results than if they were "barely" significant (*P*=0.043, for example). In addition, other researchers will need the exact *P* value if they want to combine your results with others into a .

## Under the null hypothesis, the probability is .5.

If we saw fewer than 40 or more than60 tosses, we would say we had enough evidence to reject the null hypothesis, knowing thatwe would be wrong only 5% of the time.

## To summarize, the steps for performing a hypothesis test are:

This is very helpful for me, I finally understand how to answer such a question I the exam, but I don’t understand where the 0.500 is from

And why to substract it from the z value ?!please clear this up for me as am

Just learning about hypothesis testing, I’d also appreciate if you’d explain to me more about the z tables , are they like standard tables?! For all hypothesis testing ? Am a lil lost so please help!!:(