Wednesday, April 14, 2010

ANOVA - Comparing Doing ANOVA in Excel with Doing It By Hand

ANOVA Test

Done in Excel

Compared To By Hand




ANOVA is something you would do by hand, ONLY if you absolutely had to. I remember being forced to perform these calculations by hand in statistics class when I was getting my MBA. I also remember wondering why in the world we were doing that when we all knew Excel. Still don’t have an answer to that question. It seemed a little like doing multiplication on a slide rule even though a calculator was readily available. My father once showed me his old slide rule and how facile he had become with it. It was almost magic. I never got the urge to figure it out though. Sorry Dad.

The video below shows a statistical procedure called Single-Factor ANOVA (the simplest type of ANOVA) being solved in Excel and then solved by hand. I’m hoping that the torturous hand calculations in the video only serve to more strongly contrast the ease of doing statistics in Excel.


Step-By-Step Video Showing How To Do Single-Factor ANOVA In Excel and Also How To Do It By Hand:

(Is Your Sound Turned On?)


Why Excel Is A Good Starting Point To Teach Statistics


The point of this article and the linked video is to persuade statistics teachers to focus their efforts on using tools like Excel right from the start. Slogging through those hand calculations is almost never a good thing. Probably the fastest way to make a statistics student to seriously hate statistics is to force him or her to do calculation-intensive tasks like regression and ANOVA by hand.

As an Internet marketing manager who does a lot of statistics on the job, I am SOOO glad I learned how to do all of my statistic procedures on Excel. Believe it or not, statistics is actually kind of fun when you have such a convenient tool like Excel (I’ve been called a Propeller Head more than once). There are plenty of other fine statistical tools like Minitab, SPSS, and SAS. But….I (like almost any other business manager) have a pretty good grasp of Excel. Honestly, I don’t really have no desire to learn SAS (or any other statistical software that costs thousands of dollars) when I’ve got Excel. If I can use Excel instead, you bet I’m gonna.

Here’s a little info about the ANOVA test that was run in the above video:



What Is ANOVA?

ANOVA stand for Analysis of Variance. It is a test to determine if three or more variations of each of one or more factors have an effect on a population. ANOVA tests the Null Hypothesis of each factor. The Null Hypothesis of each factor states that varying the factor has no effect on a population. The ANOVA test results in either acceptance or rejection of the Null Hypothesis within a specified degree of certainty.

The single-factor ANOVA test in the linked video evaluates whether different closing methods affect the probability that a sale will close. The Null Hypothesis states that varying the closing method does not affect the number of sales that get closed. All other factors, including the abilities of the individual salespeople, are assumed to be the same.


The Null Hypothesis

Acceptance or rejection of the Null Hypothesis can be determined by either the P Value or the F Statistic obtained by the calculations. Both the P Value and the F Statistic are equivalent to each other and are nearly interchangeable. The video provide a detailed explanation of the following: We accept the Null Hypothesis if the P Value is greater than Alpha (Alpha = 1 – Required Degree of Certainty) or, equivalently, if the calculated F Statistics is less than F Critical. We reject the Null Hypothesis if the opposite is true. Rejection of the Null Hypothesis implies that variation of the associated factor did affect the outcome.



Doing ANOVA By Hand vs. By Excel


Doing ANOVA in Excel takes just a few seconds with little possibility of error if the data is inserted correctly. Doing ANOVA by hand takes a LONG time and has LOTS of opportunities for error. Here, the above video of step-by-step ANOVA video will, hopefully, will convince you of that.



Here Is the Original Problem to Be Solved With Single-Factor ANOVA:
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A group of 4 salespeople used a different closing method exclusively each week for 3 weeks. The sales totals for each salesperson using each method are shown above. We need to determine within 95% certainty whether varying the closing method affected sales numbers or not. No other factors were varied during the 3-week duration of this test.



Here is the Problem Solved in Excel in One Step:

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The Excel output shows the P Value associated with the closing methods to be 0.0144. This is significantly less than the alpha of 0.05, so we can reject the Null Hypothesis and state with 95% that varying the closing method did affect sales totals. Remember, it took less than 10 seconds to input the data from the excel spread sheet and get the above output. Compare this to doing the same problem by hand below and arriving at the same answer.

Now, Here is The Same Problem Done By Hand

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Click On Image To See Enlarged View


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Yup, same answer as Excel, but now I've got a headache!



Hopefully This Article Touched a Nerve...

Hopefully this article touched a nerve with the poor folks out there who were forced to do ANOVA by hand in statistics class. There might even be a few statistics teachers who would rather have taught ANOVA in Excel than having had to do it by hand in front of the class room. I've had to teach ANOVA by hand to a class or two and it wasn't the funnest thing I've ever done.


If you agree or disagree with this article, let the world know with your comments below. Your input is highly valued!


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Monday, April 5, 2010

ANOVA - How To Increase Click-Through Rate Using ANOVA in Excel

ANOVA Test

Done in Excel

For Better PPC Marketing



If you have ever run a pay-per-click campaign, you’ve probably wondered which factors really made a difference in the click-through rates. Are the headlines really making a difference in CTR? Does the ad text have any affect on CTR? What about the interaction between ad text and headline?

The good news is that there is a statistical tool in Excel designed just for a test like that. The tool is called ANOVA: Two Factor With Replication. Here is a video which shows exactly how to perform this test.


Step-By-Step Video On How To Increase Your Click-Through Rate With ANOVA in Excel

(Is Your Sound Turned On?)


We Used ANOVA To Test for the Following


To sum up this test, we are determining whether one or both of two factors (headline and ad text) and/or the interaction between the two affected click-through rate. We are replicating the same test in two environments: on Google and also on Yahoo pay-per-click advertising programs. The replication creates the opportunity to evaluate of whether interaction between Headline and Ad Text affected CTR.




What Is ANOVA?

ANOVA, Analysis of Variance, is a test to determine if three or more different methods or treatments have the same effect on a population. The basic test of ANOVA is the Null Hypothesis, which states that varying a factor has no effect on the output. Each factor and the interaction between the two factors has its own separate Null Hypothesis.

The Null Hypothesis connected with the headlines states that choice of headlines has no effect on the measured output, the click-through rate. The null Hypothesis connected with the ad text states that choice of headlines has no effect on the output. The Null Hypothesis connected with the interaction between headline and ad text states that this interaction has no effect on the click-through rate.


Here's How We Ran Our ANOVA Test

The test was run as follows: 3 headlines and three sets of ad text were created. Altogether there were 9 possible combinations of headline / ad text. All 9 ads were run for approximately equal number of times on both the Google and Yahoo paid search networks. The Excel tool: ANOVA: Two Factor With Replication will then be run on the results to determine with at least 95% certainty whether headline, ad text, and/or their interaction had an effect on the click-through rate.

This is how the data needs to be organized on the Excel spread sheet. The yellow-highlighted cells are the input data for the Excel ANOVA.

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The above video shows the Click-Through Rates results and also how to insert the data into Excel so the ANOVA test can be run on the data.


How To Interpret the ANOVA Output From Excel

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The Excel output of the test is fairly simple to interpret. The linked video above shows exactly how that is done. In a nutshell, a factor (headline, ad text, or interaction between the two) is said to affect the output (click-through rate) if the P Value associated with that factor is less than the alpha. The alpha is derived from the level of certainty required. Alpha = 100% - Level of Certainty. For example, if a 95% level of certainty is required, then the alpha = 0.05 (100% - 95% = 5% or 0.05). The P Value associated with a factor equals the probability that the output occurred by chance.


The P Value Rule

As a general rule, if the P Value of a factor is less that the alpha, then we can reject that factor’s Null Hypothesis, which states that varying the factor has no effect on the output.

On the other hand, if the P Value of a factor is greater than the alpha, we cannot reject that factor’s Null Hypothesis. We cannot say that varying the factor had an affect on the output.
In this case, we are able to state with 95% certainty that the headlines and interaction affected the output but not the ad text.

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