These are the "blog" posts for the the discussion thread for my MTE514 class from teacherstep.com.
Blog #1
Discuss sampling methods that could easily be conducted in a school setting to assist students in further understanding of the pitfalls of sampling.
There are 5 types of sampling techniques that can be used by researchers. . Each one has its advantages and its pitfalls. The five type are random, systematic, stratified, cluster, and convenience sampling.
Random samples are samples that are selected by using chance methods. As long as each member of the population has an equal chance of being selected, this method is the best for obtaining a nonbiased sample.
In a systematic sample, researchers pick a certain number of subject to skip to obtain a sample. For example, every 10th production in an assembly line could be tested for defects. When using this technique, it is important to understand how subjects are arranged in order to avoid bias. For example, if subjects are order "husband, wife, husband, wife..." picking every 10th subject would give a sample that is all wives.
Stratified sampling divides the population into groups based on a characteristic that is important to the study, and then obtain data from each group. For example, high school students could be stratified by their grade level and then asked about their grade in their English class. Samples within the strata should be randomly selected.
Cluster sampling is useful when dealing with large populations. If there already grouping that occur, a few of these clusters can be study at random. Data from every subject in the cluster should be obtained. It is important determine if these clusters represent the population to avoid bias. For example, each classroom in a school can used as a cluster. Then a few classroom can be randomly selected as a cluster to obtain data from. If a 12th grade AP English class and a 10th grade Honors History class were picked, there may be a bias in the data, because these class may not be representative of the population of the school.
Convenience sampling is the techniques most used by students. It is the "man on the street" technique. This type of sampling can be very biased becauses students only tend to obtain data from people physically close to them, which tends to be their friends and family. If it can be determined that the convenience sample is representative of the population, it can be used. Otherwise, it should not.

Blog #2
Module 2 focuses on the use of different types of regression. Discuss how students interpret regression in daily use.
Regression for students is all about finding connections, hopefully predictable, between two things. For example, they might find that when their "low fuel" light comes on in their car, they still have 50 miles until they run out of gas, even if they gauge is past they empty. I might conclude that if they do their homework, their grades will go up. Or they might find that when they get a good night's sleep, they feel better they next day. If they go to a casino, they might notice that the odds are always against them and the house always wins, but people can still win money, and that's what makes it exciting.

Blog #3
Simulations are a great way to for students to see how probability distributions are found in actual data. Discuss how you would use simulations within experiments.
I use simulations to show how the central limit theorem is built. I simulate coin flips using a python program, which will then give a graph of the results. The program can simulate a few coin flips to see how the graph lines up with the binomial distribution. As I increase the number of flips it simulates, the graph keeps getting closer and closer to the normal distribution. This helps students connect the blocky histogram of the binomial distribution to the smooth curve of the normal distribution.
The other simulation I run for them is of the Monty Hall Problem. It is a very tough problem to think through logically, and even when we talk about it, the logical never seems to make sense. The program I write simulates the problems many times and give the chance of winning the car. Sometimes they still believe the logic behind it, but they trust the computer because they can see each result happening.

Blog #4
Discuss how sampling can be used to make inferences about a population.
One way sampling is used to make inferences about a population is a process called hypothesis testing. It is a decisionmaking process that evaluates certain claims about a population. For example, a drug company may wish to know if a certain drug can reduce the infection rate of HIV in MSM over another drug. Two groups of men will be selected and each group will get a different drug. At the end of the trail, the number of new HIVinfection for each group will be counted, and the hypothesis test would be run, and the data would be used to determine if the new drug was better at preventing HIV infections.
