As I mentioned last week, you can make up a single quiz (Due Tues 26 Nov) by doing the following:
1. Find a probability/statistics article on Wikipedia.
2. Read as much of it as you can. I expect you to spend somewhere between 20 and 40 minutes reading the article. Use links in the article to look up some of the terms you're unfamiliar with.
3. Write down 5 things you learned or found interesting, one sentence each.
The following 2 links are Wikipedia "Outline" articles. They show the organization of all the content related to that topic on Wikipedia, and can be a good place to start.
http://en.wikipedia.org/wiki/Outline_of_probability
http://en.wikipedia.org/wiki/Outline_of_statistics
10.29.2013
Data entry: Number of Heads and Switches
You can find the survey to enter data from today's activity here.
10.14.2013
Week 9: Confidence Intervals
In class this week we are looking at confidence intervals, starting with the proportion of successes (p) of a binomial process. p̂ is the sample estimate of p. The following figures illustrate what we did for a range of values.
This figure shows how the standard error (SE) of p̂ changes with respect to p̂ and the sample size.
This figure shows how the width of the confidence interval changes with respect to p̂, the sample size, and α. The panel headings show the "confidence", i.e. (1-α).
10.08.2013
Change in Readings
The schedule has been updated to switch the reading for the next two weeks. Next week's quiz is on CGS Ch 8, and the week after is CGS Ch 7.
10.03.2013
Lab 4: Discrete and Continuous Distributions
Lab 4 is available here. It's due at the beginning of class on Tues, 22 Oct 2013.
Week 7: Hypothesis testing, class videos
This week we're looking at hypothesis testing. We started out using the Wilcoxon rank-sum test (also known as the Mann-Whitney U test) to test whether samples were drawn from different populations.
The world is full of statistical (hypothesis) tests. Each one generates a test statistic. The key to understanding a test is understanding what the distribution of the test statistic would be if the null hypothesis was true.
The test statistic of the rank sum test is U: the sum of the ranks minus a sample size correction factor.
For the rank sum test, the null hypothesis is (approximately) that two samples are drawn from populations with the same mean. The following figures show the distribution of U, assuming the null hypothesis is true. The area of the shaded region sums to alpha. The vertical red lines show our critical values of U. Values of U that are more extreme than these critical values are unlikely due to chance if the null hypothesis is true. Thus, if we observe U values this extreme, we can reject the null hypothesis.
If we lower alpha, we see the area in the tails get smaller.
For larger sample size, we see the value of U gets much larger, but the same pattern holds.
For a devil's advocate view of what p-values mean, we turn to the internet:
What the p-value
The Mann-Whitney U test (also known as the Wilcoxon rank sum test) is a non-parametric test: it makes no assumptions about the distribution of the data. Most common statistical tests are parametric, and usually assume the data (or something about the data) is normally distributed. The t-test is the parametric sibling of the rank sum test. It assumes the data is normally distributed.
This video describes hypothesis tests in general, and walks through the t-test.
What is a t-test?
By the end of this week, this comic should make sense.
XKCD: Significant
The world is full of statistical (hypothesis) tests. Each one generates a test statistic. The key to understanding a test is understanding what the distribution of the test statistic would be if the null hypothesis was true.
The test statistic of the rank sum test is U: the sum of the ranks minus a sample size correction factor.
For the rank sum test, the null hypothesis is (approximately) that two samples are drawn from populations with the same mean. The following figures show the distribution of U, assuming the null hypothesis is true. The area of the shaded region sums to alpha. The vertical red lines show our critical values of U. Values of U that are more extreme than these critical values are unlikely due to chance if the null hypothesis is true. Thus, if we observe U values this extreme, we can reject the null hypothesis.
If we lower alpha, we see the area in the tails get smaller.
For larger sample size, we see the value of U gets much larger, but the same pattern holds.
For a devil's advocate view of what p-values mean, we turn to the internet:
What the p-value
The Mann-Whitney U test (also known as the Wilcoxon rank sum test) is a non-parametric test: it makes no assumptions about the distribution of the data. Most common statistical tests are parametric, and usually assume the data (or something about the data) is normally distributed. The t-test is the parametric sibling of the rank sum test. It assumes the data is normally distributed.
This video describes hypothesis tests in general, and walks through the t-test.
What is a t-test?
By the end of this week, this comic should make sense.
XKCD: Significant
10.02.2013
Week 6 survey results: reaction times
Here's a familiar histogram of each person's reaction times (in distance), along with everyone combined together (heading "All").
Overall, the whole class (heading "All") appears approximately normally distributed, though somewhat right-skewed. Why might we expect this distribution to be right (upwards) skewed?
With this 3-column layout, it is difficult to compare individual performances. We could use one column and 15 rows, but that would make a very long figure. The following figure condenses each person's data, easing comparisons. This is called a box-and-whisker plot, or boxplot. The black dot shows the median, and the box shows the interquartile range (which measures the variability, similar to standard deviation). The individual points are considered outliers. For more information, see the boxplot wikipedia page.
From this, I can easily see some people's responses vary quite a bit, while others are much more consistent. I also notice that 2 people appear faster (lower distance) than the average, and one person appears slower. How might we test if these are significantly different from the rest of the class?
Overall, the whole class (heading "All") appears approximately normally distributed, though somewhat right-skewed. Why might we expect this distribution to be right (upwards) skewed?
With this 3-column layout, it is difficult to compare individual performances. We could use one column and 15 rows, but that would make a very long figure. The following figure condenses each person's data, easing comparisons. This is called a box-and-whisker plot, or boxplot. The black dot shows the median, and the box shows the interquartile range (which measures the variability, similar to standard deviation). The individual points are considered outliers. For more information, see the boxplot wikipedia page.
From this, I can easily see some people's responses vary quite a bit, while others are much more consistent. I also notice that 2 people appear faster (lower distance) than the average, and one person appears slower. How might we test if these are significantly different from the rest of the class?
Subscribe to:
Posts (Atom)