Example: Chi-Squared Test

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En provenance du cours de University of Washington

Practical Predictive Analytics: Models and Methods

286 notes

University of Washington

Practical Predictive Analytics: Models and Methods

286 notes

Cours 2 sur 4 dans Specialization Data Science at Scale

Statistical experiment design and analytics are at the heart of data science. In this course you will design statistical experiments and analyze the results using modern methods. You will also explore the common pitfalls in interpreting statistical arguments, especially those associated with big data. Collectively, this course will help you internalize a core set of practical and effective machine learning methods and concepts, and apply them to solve some real world problems. Learning Goals: After completing this course, you will be able to: 1. Design effective experiments and analyze the results 2. Use resampling methods to make clear and bulletproof statistical arguments without invoking esoteric notation 3. Explain and apply a core set of classification methods of increasing complexity (rules, trees, random forests), and associated optimization methods (gradient descent and variants) 4. Explain and apply a set of unsupervised learning concepts and methods 5. Describe the common idioms of large-scale graph analytics, including structural query, traversals and recursive queries, PageRank, and community detection

À partir de la leçon

Practical Statistical Inference

Learn the basics of statistical inference, comparing classical methods with resampling methods that allow you to use a simple program to make a rigorous statistical argument. Motivate your study with current topics at the foundations of science: publication bias and reproducibility.

Outliers and Rank Transformation3:24

Example: Chi-Squared Test3:39

Bad Science Revisited: Publication Bias4:47

Effect Size4:26

Meta-analysis5:05

Fraud and Benford's Law4:09

Intuition for Benford's Law2:50

Benford's Law Explained Visually3:50

Rencontrer les enseignants

Bill Howe
Director of Research
Scalable Data Analytics

I want to give you another example of how to apply these resampling methods

in a different kind of statistical inference context.

So the Chi-Squared Test is used for categorical data.

So for example, what is the relationship between health and wealth,

where we define health in terms of three categories, poor, middle class, and

rich, and wealth in terms of, let's say, sick or healthy?

And we perhaps do a survey to get tallies of each one of these categories.

And we wanna try to understand the relationship here.

The chi-squared test is used when we're trying to measure

the relationship between two variables or

the difference in observation from the expected distribution.

So if we tabulate these results like we have here.

We have the measured count of those who reported being both sick and poor is 20,

and so on.

How do we compute the expected value that we're gonna measure the difference from?

Well if these two variables, health and

wealth, are independent, then we'd expect the same ratio of sick to healthy

exhibited in the poor to be the same ratio of sick to healthy in middle and

the same ratio of sick to healthy in rich, that it would have no affect.

And so what we can do is, count up the total number of overall subjects we have,

110, and take the ratio of sick over 110.

There's 46 sick over 110 total.

And then multiply that by the number of poor, and

that's the expected number of both poor and sick, which is 18.48, and

we can repeat that for each one of the combinations of variables.

And then subtract the expected value from our measured value to get a marginal,

a residual rather, and then square that and then

divide it again by the expected value, and that's the chi squared statistic.

And then we add that all up for the overall case, the overall experiment.

The overall data set, in order to get this drive statistic.

And then this is the statistics we want to do the significance test on.

So how do we do that?

Well, we talked about shuffling the labels and

we talked about boot strap resampling methods.

Here what you can notice is the calculation depends on

the marginal values here.

The total number of sick, the total number of poor,

the total in the middle and so on.

So what you want to do is design a relabeling, a shuffle

process that will keep the marginals the same,

but should still change the value in order to allow you to do the test.

So the way to think about this is that each observation

has a single label rather than two labels.

It has the sick/poor label, or the sick/middle label, or the sick/rich label,

or the healthy/poor label, or the healthy/middle label, or

the healthy/rich label, and sort of concatenate these two labels together.

Then you can do a shuffle test as usual.

And the marginals will then necessarily stay the same.

The total number of poor will stay the same and

the total number of healthy will stay the same and so on.

One other thing I should mention about the Chi-Squared test is

it's only valid if every category has at least ten observations in it,

it has fewer than that then it's invalid to use.

The sample won't be distributed in Chi-Squared.

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