Testing Hypotheses, Part 2: An Example Application

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Del curso dictado por University of California, Davis

Quantitative Research

25 calificaciones

University of California, Davis

Quantitative Research

25 calificaciones

Curso 3 de 4 en SpecializationMarket Research

In this course, you will obtain some insights about marketing to help determine whether there is an opportunity that actually exists in the marketplace and whether it is valuable and actionable for your organization or client. Week 1: Assess methods available for creating quantitative surveys, along with their advantages and disadvantages. Identify the type of questions that should be asked and avoid unambiguous survey questions. Week 2: Design, test, and implement a survey by identifying the target audience and maximizing response rates. You will have an opportunity to use Qualtrics, a survey software tool, to launch your own survey. Week 3: Analyze statistical models that can be applied to your marketing data, so that you can make data-driven decisions about your marketing mix. Week 4: Predict most likely outcomes from the marketing decisions and match the type of analysis needed for your business problem. Take Quantitative Research as a standalone course or as part of the Market Research Specialization. You should have equivalent experience to completing the second course in this specialization, Qualitative Research, before taking this course. By completing the third class in the Specialization, you will gain the skills needed to succeed in the full program.

De la lección

Analyzing a Survey

In this module, you will be able to review your survey data and look for any errors. You will be able to analyze your survey conducting descriptive and inferential analysis techniques to test your hypotheses. You will be able to conduct association analysis and causal analysis with your data. Please note that this module features a fair amount of advanced statistics related math. Throughout the module, optional activities setup as practice quizzes have been provided to help reinforce what you're learning.

Analyzing a Survey Introduction1:09

Reviewing Your Data and Looking for Errors4:47

The Importance of Scales5:50

Descriptive Analysis: Nominal Data6:14

Descriptive Analysis: Ordinal and Interval Data5:21

Inferential Analysis: Confidence Interval6:27

Testing Hypotheses, Part 1: Overview3:27

Testing Hypotheses, Part 2: An Example Application6:40

Association Analysis: Comparing Groups of People4:37

Association Analysis: Chi-Square Test6:02

Association Analysis: Correlation Analysis2:01

Causal Analysis6:15

Conoce a los instructores

Susan Berman
President, Impact Research
UC Davis Division of Continuing and Professional Education
Olivier Rubel, PhD
Associate Professor, Graduate School of Management
UC Davis

Previously, we discussed formulating and testing a hypothesis.

In this lesson, we will go a bit further using an example.

Coming back to the Burger King example,

suppose that the company,

based on previous studies on the willingness to pay for it's new burger,

found that the willingness to pay is $6.45.

And these studies have been done nationwide.

Now, Burger King wants to see if this willingness to pay for

the new burger is different or the same for West Coast markets in the United States.

So the question would be, do I use the same price or do I want

to have a different price for the West Coast?

Suppose that you administer a survey of respondents from the West Coast

and that the sample size is representative of the West Coast markets: California,

Washington State, and Oregon State.

So survey indicates that respondents, on average,

revealed that their willingness to pay for

the new burger is actually going to be about $7.

The marketing question here is,

can I conclude, based on this data,

that the willingness to pay on the West Coast is different,

and in fact, higher than the national level?

Here, I need to give you two additional pieces of information to move forward.

One is that the sample size is 1,000 and that the standard deviation is 1.3.

The first step is to formulate the statement that you think is

true of the population on the West Coast.

I need to formulate my hypothesis.

In this case, the null hypothesis, H0,

is that willingness to pay,

WTP, is equal to $6.45.

The alternative hypothesis, the hypothesis that you want to test,

is whether this willingness to pay is different in

the West Coast than in the overall population, the rest of the country.

And so that is the question you want to have in mind,

Is my willingness to pay different than $6.45?

What we want to do is to formulate the population's willingness to pay,

mu, is equal to $6.45.

The alternative hypothesis is that this willingness to pay is different than $6.45.

Again, what is common here is that we are going to use a 95% confidence level.

The next step is to compute the sample statistic which is given by the formula,

Z equal to X bar, the sample mean,

minus mu, the population parameter that we want to make an inference on, divided by S,

the standard deviation which is itself divided by the square root of n,

n being the sample size.

So, when I compute this number,

it's basically 7.01 minus 6.45

divided by 1.3 divided by square root of 1,000.

And that gives you about 13.6.

Now, the question is what do I do with this 13.6?

Based on the Z value for 95% confidence level,

I want to compare this number to the Z value

to the theoretical value at the 95% confidence level.

This value can be easily found in any statistical textbook or online and is 1.96.

Again, bear in mind that it turns out that this is the same 1.96 that we had before.

So, the decision rule is as follows: if your sample statistic

is greater than the theoretical value that is based on your confidence level,

then you can reject the null hypothesis

which means that the alternative hypothesis is supported.

So it's a bit of a coverted way of presenting this information.

But the basic heuristic is that this is good news.

If your sample statistic is greater than your theoretical value which is,

here in this case,

1.96, it means that you are in good shape.

Alternative hypothesis is supported by the data and you can

reject the null hypothesis with a 95% confidence level.

Here, 13.6 is greater than 1.96 which means that we can reject the null hypothesis.

Said differently, this means that the willingness to pay for

the new burger for the West Coast markets is higher than from the rest of the country.

The opposite conclusion would be true if you had

the sample statistics lower than the theoretical value Z.

In this case, the conclusion would have been that you cannot reject

the null hypothesis which means that

the alternative hypothesis is not supported in your data.

As you can imagine,

making such inferences can be prone to some statistical errors.

Specifically, there are two types of errors.

When you test hypotheses,

you have four potential scenarios.

So, first scenario is that the null hypothesis is actually true in

the population and the test tells you that you cannot reject the null hypothesis.

That means that the null hypothesis is correct and that,

in this case, you did not make a mistake.

Another scenario is that the null hypothesis is not true in

the population and the test tells you that you should reject it.

It's good news as well because it means that the test was correct.

Now, there are two tricky situations.

One situation would be that the null hypothesis is actually true in the population.

However, the test tells you that it is not and recommend to reject it.

It means that the test is incorrect.

Since the test is based on limited data,

it incorrectly infers that the null hypothesis is not supported and

the whole point here is to say that the null hypothesis is true

but the statistical tests tells you it is not.

That is called the Type 1 error.

As you can guess, the last possible scenario refers to a situation where

the null hypothesis is not true in the overall market but the test tells you otherwise.

This type of error is called the Type 2 error.

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