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Business 110: Business Math10 chapters | 78 lessons | 10 flashcard sets

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Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Watch this video lesson to learn about statistical significance, and how it relates to surveys and other real world events. Also, learn how it is calculated, and how you can describe it to others.

You have probably answered a survey at least once in your life. Anything can be a survey if you think about it. As long as the same question is asked of different people, it can be considered a survey. Formal surveys conducted by scientists and researchers have a set of questions that are then given to a large number of different people. These questions can be in the form of written questions, or they can be verbal questions performed in an interview, or they can even be tests performed on people to see what kinds of results are achieved. Psychologists, for example, may perform a survey in which they record the reaction of others to a particular scenario, such as a person standing facing the back wall in an elevator instead of facing towards the door.

Many tests and surveys are performed every day by various people, but not all of these end up being useful. Why is this? It is because for a survey to be considered useful it must have **statistical significance**, a low probability that the hypothesis is not true. In other words, a statistically-significant survey will have a high probability of a hypothesis being true.

For example, if our survey shows that 99% of respondents, people who responded, drive a four-door sedan, we can say that this survey is statistically-significant because the hypothesis that most people drive four-door sedans has a high probability of being true according to the survey. However, you won't see the 99% when talking about statistical significance.

Instead, you will see a **p-value**, the probability that the hypothesis is not true. This p-value is a decimal number between 0 and 1. These p-values are found by referring to charts and tables related to the kind of survey you perform.

The accepted p-value that makes a hypothesis statistically significant is 0.05. If our p-value is less than 0.05, then we can assume the hypothesis to be true, for the most part. If our p-value is greater than 0.05, then the hypothesis cannot be relied on and it is thrown out. What does this p-value mean? A p-value of 0.05 tells you that the probability of the hypothesis being false is 0.05 or 5%. 5% translates to once every 20 times. So a hypothesis with a p-value of 0.05 means that the hypothesis is false once every 20 times.

You can see that if the p-value is even smaller, then there is even less chance of our hypothesis being false. For example, a p-value of 0.01 means that there is a probability of 1% that the hypothesis will be false, that the hypothesis is false once every 100 times.

I have to tell you, though, that just because a hypothesis is statistically significant, that it has a p-value less than 0.05, does not mean that the hypothesis is something you can rely on for all time. If the sample size, the number of people questioned, is small, then the p-value can very well be less than 0.05 but the hypothesis cannot be generalized to all people since the answers of that small group of people may be unique to that group. Statistical significance is just a mathematical way to determine whether a hypothesis is worth looking deeper into. When a hypothesis is found to be statistically significant, further studies and surveys can be conducted to see if the hypothesis is still statistically significant for a larger population.

We can translate this p-value into the probability of our hypothesis being true by subtracting the p-value from 1. A p-value of 0.05, then, will have a probability of 1 - 0.05 = 0.95 or 95% of being true. A p-value of 0.01 will have a probability of 1 - 0.01 = 0.99 or 99% of being true. Converting the p-value into the probability of a hypothesis being true might be easier to grasp mentally. You can easily see that the smaller the p-value, the greater the chance of our hypothesis being true.

For problems, you can make this conversion as long as you keep in mind that it is the p-value that matters and not the probability that something is right. And remember that the p-value gives you the probability of a hypothesis being false.

All this information is useful in business when looking at your statistics. If you find your p-value, you can decide whether to pay attention to the statistic or not. For example, if the statistic that only 10% of your customers are teenagers has a p-value of 0.1, then you can ignore this statistic because its p-value is greater than 0.05. However, if the statistic that 90% of your customers are elderly has a p-value of 0.03, then this statistic is worth looking into. You might want to gear your business more towards the elderly.

Let's review what we've learned:

We learned that **statistical significance** is a low probability that the hypothesis is not true. To determine whether a hypothesis is statistically significant, we use the **p-value**, the probability that the hypothesis is not true.

The standard p-value for statistical significance is 0.05. If the p-value is less than 0.05, then the hypothesis is statistically significant. If the p-value is greater than 0.05, then the hypothesis is not statistically significant, and we can disregard it. To convert the p-value into a value that tells us the probability of the hypothesis being true, we subtract the p-value from 1.

Following this lesson, you should have the ability to:

- Explain what statistical significance is and its importance
- Define p-value
- Identify the p-value for statistical significance
- Describe how to use the p-value

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Business 110: Business Math10 chapters | 78 lessons | 10 flashcard sets

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