Today, we'll discuss how to interpret the result of Anova and connect it to our action.
[Intro Video]
Hi, this is Mike Negami, Lean Sigma, Black Belt.
In the last video, we went up to producing the result of Two-Factor Anova, with the Excel
Data Analysis Tools.
A quick recap from the last video, the data on the left is the score data that was rated
by 60 people for 4 prototypes of fried chicken dishes in a restaurant.
The data consists of the factor of 'Texture' such as ""Crispy"" and 'Regular' and another
factor of 'Seasoning' such as 'Spicy' and 'Standard'.
I converted the data format from the flat format to the cross-tabulation format.
Then, click 'Data', 'Data Analysis', and 'Anova: Two-Factor With Replication'.
A lot of numbers came out.
Of course, it’s better to understand the meaning of all the numbers, but today, I'll
give you the minimum information needed to use ANOVA in practice.
I added the same table to the right.
The yellow highlighted parts are the most important.
I added Excel functions in to that table to get the same results as in the table on the
left, so that you can learn a bit deeper about the Anova results for yourself.
You can download this Excel file from this video’s description below for your study,
so please check what each value means later.
The first three tables are not so difficult, but the last one may be challenging.
It's called the 'Anova Table'.
Of course, it's good if you understand all numbers in the table, but at least understand
this 'P-Value' well.
I talked about this 'P-Value' in the videos about Regression Analysis.
In more detail, P-value is the probability of the null hypothesis to occur.
The 'P' in P-value stands for ‘Probability’.
The null hypothesis in Anova is “Assuming that the means of the data groups of each
factor are equal"".
Our null hypothesis would be “No difference in the scores of the four prototype dishes.”
Generally, if this percentage is 5% or less, you can reject a null hypothesis.
In other words, discarding that ""the averages are same"" means ""the differences between
the averages of the data groups are significant"".
With this in mind, let's look at the our Anova table.
It says 'Columns' here.
That refers to the vertical direction, in our case, Crispy and Regular, in the columns.
Their P-value is 0.36, which is 36% and more than 5%, so we cannot reject the null hypothesis.
In other words, it means that whether it is Crispy or Regular, it doesn't affect the scores.
Next, it says 'Sample' above.
That refers to the horizontal direction, Spicy and Standard.
Their P-value is 0.08, which is 8%.
This is lower possibility than the last one, but since it's still higher than 5%, we cannot
say that there were differences in scores between Spicy and Regular alone.
Lastly, let's see the ‘Interaction’ below.
Its P-value is 0.01, which is 1%.
Since it's below 5%, we can reject the null hypothesis.
In other words, we cannot say that there are no differences, which means there are differences.
Based on this, let's look at the averages of each prototype’s scores.
The Spicy Crispy Chicken has the highest score.
We already knew that that Interaction has a significant difference in the scores, so
we can conclude that it would be better to sell it in the form of Spicy Crispy rather
than just making it Spicy or Crispy alone.
By the way, I borrowed the data from the web page of ""Fun statistics studied at a hamburger
shop"".
It's in Japanese, and I put the site's URL in this video’s description below.
In today's example, that data has two factors, but each factor has only 2 levels, so we could
judge the superiority or inferiority between levels by Anova and averages.
However, if there are three or more levels in one factor, and even if you could reject
your null hypothesis, you can just say that “the averages of all data groups are not
equal”, but you cannot identify which ‘Between Group’ has a significant difference.
Then, if there are more than two levels in one factor, can't we use Anova?
Yes, we can.
You can use Anova when you want to find out if your data groups don't have differences.
Now, what if there are more than two levels and you want to find out where is a difference?
Although Excel Data Analysis Tools don’t include this function, you can do a ‘Multiple
Comparison Analysis’ using Excel functions.
However, you need advanced knowledge of statistics such as multiplicity, etc.
I may make a video about this if I receive request.
This Anova content may be very confusing, so I summarized it in the table.
This is only the case when using Excel.
When there are only two data groups to compare, meaning there is only one factor with two
levels, you can use T-test.
If there is one factor but three or more levels, you can use One-Factor Anova, but this is
when you want to find out if there is no difference.
When there are two factors with 2 levels each, you can use Two-Factor Anova.
You can still use Anova when you want to check that there is no difference in the data groups
with two factors with levels of 3 or more, but if you want to know the details in the
data, you have to use Multiple Comparison Analysis.
This time I've simplified the very difficult contents considerably.
Statistics experts, however, may have other opinions, so please put those in the comment
section below, because I would like to deepen the discussion with you.
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