Question

testing a scientific hypothesis involves four main steps. examine each of these steps in detail.

Answer 1

Steps in Hypothesis Testing

Step 1: State the Hypotheses

Step2: Collect Data, Check Conditions, and Summarize Data

Step 3: Assess the Evidence

Step 4: Making Conclusions

Hypotheses testing step 1-

In all three examples, our aim is to decide between two opposing points of view, Claim 1 and Claim 2. In hypothesis testing, Claim 1 is called the null hypothesis (denoted “Ho“), and Claim 2 plays the role of the alternative hypothesis (denoted “Ha“). As we saw in the three examples, the null hypothesis suggests nothing special is going on; in other words, there is no change from the status quo, no difference from the traditional state of affairs, no relationship. In contrast, the alternative hypothesis disagrees with this, stating that something is going on, or there is a change from the status quo, or there is a difference from the traditional state of affairs. The alternative hypothesis, Ha, usually represents what we want to check or what we suspect is really going on.

Hypothesis Testing Step 2: Collect Data, Check Conditions and Summarize Data

This step is pretty obvious. This is what inference is all about. You look at sampled data in order to draw conclusions about the entire population. In the case of hypothesis testing, based on the data, you draw conclusions about whether or not there is enough evidence to reject Ho.

There is, however, one detail that we would like to add here. In this step we collect data and summarize it. Go back and look at the second step in our three examples. Note that in order to summarize the data we used simple sample statistics such as the sample proportion (p-hat), sample mean (x-bar) and the sample standard deviation (s).

In practice, you go a step further and use these sample statistics to summarize the data with what’s called a test statistic. We are not going to go into any details right now, but we will discuss test statistics when we go through the specific tests.

This step will also involve checking any conditions or assumptions required to use the test.

Hypothesis Testing Step 3: Assess the Evidence

As we saw, this is the step where we calculate how likely is it to get data like that observed (or more extreme) when Ho is true. In a sense, this is the heart of the process, since we draw our conclusions based on this probability.

• If this probability is very small (see example 2), then that means that it would be very surprising to get data like that observed (or more extreme) if Ho were true. The fact that we did observe such data is therefore evidence against Ho, and we should reject it.
• On the other hand, if this probability is not very small (see example 3) this means that observing data like that observed (or more extreme) is not very surprising if Ho were true. The fact that we observed such data does not provide evidence against Ho. This crucial probability, therefore, has a special name. It is called the p-value of the test. 4. hypothesis testing step 4- Conclusions-

• Since our statistical conclusion is based on how small the p-value is, or in other words, how surprising our data are when Ho is true, it would be nice to have some kind of guideline or cutoff that will help determine how small the p-value must be, or how “rare” (unlikely) our data must be when Ho is true, for us to conclude that we have enough evidence to reject Ho.

  This cutoff exists, and because it is so important, it has a special name. It is called the significance level of the test and is usually denoted by the Greek letter α (alpha). The most commonly used significance level is α (alpha) = 0.05 (or 5%). This means that:

• if the p-value < α (alpha) (usually 0.05), then the data we obtained is considered to be “rare (or surprising) enough” under the assumption that Ho is true, and we say that the data provide statistically significant evidence against Ho, so we reject Ho and thus accept Ha.
• if the p-value > α  (alpha)(usually 0.05), then our data are not considered to be “surprising enough” under the assumption that Ho is true, and we say that our data do not provide enough evidence to reject Ho (or, equivalently, that the data do not provide enough evidence to accept Ha).