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This post is following of the above post. In this post I will do simulation based statistical inference with R infer package.
First, I load infer package.
I refere website of Tidy Statistical Inference • infer
First, I will check "whether change are related to Region or not."
I calculate obserbed F statistic.
Then, I generate null distribution using randomization simulation.
Let's visualize null distribution and observed F statistic.
It seems there is not statistically significant relationship between change and Region.
Let's calculate p-value.
p-value is 0.291, it is grater than 0.05. So, it is not statistically significant relationship between change and Region.
To confirm that, I also do formula based ANOVA with aov() function and summary() function.
With formula based, p-value is 0.293. So, the conclusion is not changed.
Next, let's check whether change and IncomeGroup has relationship or not.
I calculate obserbed F statistic.
Next, I generate null distribution.
I visualize null distribution and obserbed F statistic.
It seems there is statistically significant relationship.
Let's calculate p-value.
p-value is 0.006, which is smaller than 0.05. So, there is statistically relationship between change and IncomeGroup.
How about formula based ANOVA?
p-vale by formula based ANOVA is 0.00381, so it indicates significantly relationship.
Then, let's check change and sulums_2000.
First, I calculate obserbed slope.
Then, I calculate null distribution.
I visualize null distribution and observed slope.
It seems there is statistically relationship between change and sulums_2000.
Let's calculate p-value.
p-value is 0, so there is surely statistically significant relationship.
Let's do formula based regression inference with lm() function and summary() function.
With formula based regression inference, p-value is 1.91e-08. So it is statistically significant.
In this post I clonclude there is statistically relationship between change and IncomeGroup, change and sulums_2000, there is not statisticall significant relationship between change and Region.
That's it! Thank you!
Next post is
To reard from the first post,
