Hypothesis Tests: Null and Alternative Hypothesis

00:01 Hi. And welcome back.

00:03 This section is based on the knowledge that you acquired previously.

00:07 So if you haven't been through it, you may have a hard time keeping up.

00:11 Make sure you have seen all the videos about confidence intervals, distributions, Z tables and T tables and have done all the exercises.

00:20 If you've completed them already, you are good to go.

00:24 Confidence intervals provide us with an estimation of where the parameters are located. However, when you are making a decision, you need a yes or no answer. The correct approach in this case is to use a test.

00:38 In this section, we will learn how to perform one of the fundamental tasks and statistics. Hypothesis testing.

00:46 Okay. There are four steps in data driven decision-making.

00:51 First, you must formulate a hypothesis.

00:56 Second, once you have formulated a hypothesis, you will have to find the right test for your hypothesis.

01:03 Third, you execute the test.

01:06 And fourth, you make a decision based on the results.

01:11 Let's start from the beginning.

01:13 What is a hypothesis? Though there are many ways to define it.

01:18 The most intuitive I've seen is a hypothesis is an idea that can be tested.

01:26 This is not the formal definition, but it explains the point very well.

01:31 So if I tell you that apples in New York are expensive.

01:34 This is an idea or a statement, but is not testable until I have something to compare it with.

01:42 For instance, if I define expensive as any price higher than $1.75 per pound, then it immediately becomes a hypothesis.

01:54 What's something that cannot be a hypothesis.

01:57 An example may be would the USA do better or worse under a Clinton administration compared to a Trump administration? Statistically speaking, this is an idea, but there is no data to test it.

02:11 Therefore it cannot be a hypothesis of a statistical test.

02:16 Actually, it is more likely to be a topic of another discipline.

02:21 Conversely, in statistics we may compare different US presidencies that have already been completed, such as the Obama administration and the Bush administration, as we have data on both.

02:33 All right. Let's get out of politics and get into hypotheses.

02:38 Here's a simple topic that can be tested.

02:41 According to Glassdoor, the popular salary information website, the mean data scientist salary in the US is 113,000.

02:51 So we want to test if their estimate is correct.

02:56 There are two hypotheses that are made.

02:58 The null hypothesis denoted h zero and the alternative hypothesis denoted h one or h a.

03:08 The null hypothesis is the one to be tested, and the alternative is everything else. In our example, the null hypothesis would be. The mean data scientist salary is 113,000.

03:24 While the alternative, the mean data scientist salary is not 113,000. Now you would want to check if 113,000 is close enough to the true mean predicted by our sample. In case it is, you would accept the null hypothesis.

03:43 Otherwise, you would reject the null hypothesis.

03:47 The concept of the null hypothesis is similar to innocent until proven guilty. We assume that the mean salary is $113,000 , and we try to prove otherwise.

04:01 Okay. This was an example of a two-sided or a two-tailed test.

04:06 You can also form one-sided or one tale tests.

04:10 Say Your friend Paul told you that he thinks data scientists earn more than $125,000 per year.

04:18 You doubt him? So you design a test to see who's right.

04:23 The null hypothesis of this test would be the mean data scientist salary is more than 125,000.

04:32 The alternative will cover everything else.

04:34 Thus, the mean data scientist salary is less than or equal to 125,000. It is important to note that outcomes of tests refer to the population parameter rather than the sample statistic. So the result that we get is for the population.

04:53 Another crucial consideration is that generally the researcher is trying to reject the null hypothesis.

05:00 Think about, the null hypothesis has the status quo and the alternative as the change or innovation that challenges that status quo.

05:09 In our example, Paul was representing the status quo, which we were challenging.

05:15 Let me emphasize this once again, in statistics.

05:18 The null hypothesis is the statement we are trying to reject.

05:21 Therefore, the null hypothesis is the present state of affairs, while the alternative is our personal opinion.

05:29 It truly is counterintuitive in the beginning, but later on when you start doing the exercises, you will understand the mechanics.

05:38 Okay. After this lecture, there will be a detailed comment on these two examples.

05:43 In addition, make sure you complete the quiz questions, so you become confident with forming hypotheses.

05:51 Thanks for watching.