Recent questions in Types of Bias

Research MethodologyAnswered question

wijii4 2022-09-24

So in my stats book I am told the following: A type I error is a false positive meaning you reject the null hypothesis when it's true. A type II error is a false negative meaning you reject the alternative hypothesis when it's true. My question is what causes these errors to occur? Is it simply bad sampling methods resulting in your getting biased data that causes you to get a skewed test statistic value and make the wrong conclusions? What causes these types of errors in hypothesis testing?

Research MethodologyAnswered question

Sandra Terrell 2022-08-10

Let $A$ and $B$ be some continuous random variables. We proceed as follows: we take a coin with bias $b$ and flip it. If heads, we inspect $A$, if tails we inspect $B$. Call this resulting random variable $C$.

Now say I can observe $C$ and want to figure out if the coin was heads or tails, i.e. I want to compute $Pr[$

One thought I had was to approximate the coin toss with a continuous random variable $K$ with pdf:

$k(x)=b,{\textstyle \text{for}}x\in [-1,0]$

$k(x)=1-b,{\textstyle \text{for}}x\in [0,1]$

Then one could compute the joint density function for $K$ and $C$ and compute $Pr[K<0|C=c]$ from there. But this looks clunky and ugly. Is there a better way?

Now say I can observe $C$ and want to figure out if the coin was heads or tails, i.e. I want to compute $Pr[$

One thought I had was to approximate the coin toss with a continuous random variable $K$ with pdf:

$k(x)=b,{\textstyle \text{for}}x\in [-1,0]$

$k(x)=1-b,{\textstyle \text{for}}x\in [0,1]$

Then one could compute the joint density function for $K$ and $C$ and compute $Pr[K<0|C=c]$ from there. But this looks clunky and ugly. Is there a better way?

Research MethodologyAnswered question

Brenton Dixon 2022-07-21

There is a box with $12$ dice which all look the same. However there are actually three types of dice:

$6$ normal dice. The probability to get a $6$ is $1/6$ for each dice.

$3$ biased dice. The probability to get a $6$ is $0.85$.$3$ biased dice. The probability to get a $6$ is $0.05$.You take a die from the box at random and roll it.What is the conditional probability that it is of type $b$, given that it gives a $6$?

$6$ normal dice. The probability to get a $6$ is $1/6$ for each dice.

$3$ biased dice. The probability to get a $6$ is $0.85$.$3$ biased dice. The probability to get a $6$ is $0.05$.You take a die from the box at random and roll it.What is the conditional probability that it is of type $b$, given that it gives a $6$?

Bias is an important concept in statistics and mathematics that occurs when data is not collected or analyzed fairly. There are three main types of bias: sampling bias, measurement bias, and selection bias. Sampling bias occurs when the sample used to make a conclusion is not representative of the population, measurement bias is when measuring devices are not accurate, and selection bias occurs when the data is chosen in a way that affects the results. To eliminate bias, it is important to use random sampling, reliable measurement devices, and unbiased selection criteria. With these strategies, you can ensure that your data is bias-free and your math equations are accurate.