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Course Content 1) Exploratory Data Analysis 2) Probability Theory 3) Random Variables 4) Distributions 5) Generating Functions 6) Joint Distributions 7) Conditional Expectations 8) CLT 9) Sampling & Inference 10) Point Estimation 11) Confidence Intervals 12) Hypothesis Testing 13) Regression and Correlation 14) ANOVA For exams: Exam P CS1 Formerly CT3 ----------------------------- Lets Keep in Contact ----------------------------- Hit the subscribe button if you would like to see more on Youtube. Join our Actuarial Science Community on Facebook - https://bit.ly/2AyCN1p MJ’s Udemy courses - https://bit.ly/2AyCUtR MJ’s awesome actuarial T-shirt designs - https://bit.ly/2Q3FKML [TUT] Type I Error, The Size of the Test Hypothesis Testing is prone to two types of errors. In this tutorial, we will discuss Type I, and in the next tutorial, we will discuss Type II. Type I, also known as the size of the test is formally stated as: The probability that we reject the null hypothesis given that the hypothesis is true. We use the Greek letter of alpha to represent this value. The null hypothesis is a guess of a random variable. The greater the difference between the observed value and the null hypothesis, the more likely the null hypothesis is false, but the null hypothesis is never false with absolute certainty because it follows the normal distribution. The normal distribution has infinite limits, and thus each value has a likelihood of occurring. Practically the normal distribution has thin tails meaning that not much probability weight is kept in the tails. This means we can create reasonably narrow confidence intervals that are statistically significant. A Type I error occurs when the parameter does have an expected value that is equal to the null hypothesis, but due to statistical fluctuation, it is observed to have a value that exceeds the confidence interval. Traditionally we can control the probability of the Type I error by stating that we want our confidence interval to be 95%. This means that alpha is equal to 5% and we use this value to calculate what the confidence values should be. Sometimes we might reduce Type I error by making our confidence interval 99%. However, this increases the width of the confidence interval and increases the probability of a Type II error which we shall discuss in the next tutorial. The terminology might be tricky. I’ve used terms like confidence intervals here, but in the video, I refer to them as critical regions. You must be familiar with both. Check out the video for another look at these errors and more tutorials on statistics, make sure to check out Actuarial Statistics on Udemy. ******************************************************************************************************** [TUT] Type II Error, The Power of the Test Hypothesis Testing is prone to two types of errors. In this tutorial, we will discuss Type II, and in previous tutorial, we discussed Type I. Type II, also known as the power of the test is formally stated as: The probability that we fail to reject the null hypothesis given that the null hypothesis is false. We use the Greek letter of beta to represent this value. Remember from the last tutorial; the null hypothesis is a guess of a random variable. The smaller the difference between the observed value and the null hypothesis, the more likely the null hypothesis is true, but the null hypothesis is never true with absolute certainty because competing hypotheses also follow the normal distribution. The normal distribution has infinite limits, and thus each value has a likelihood of occurring. Thus there is always a chance that the observed value is within the confidence interval of the null hypothesis but actually belongs to another hypothesis. This means that an observed value of our random variable might be close to the null hypothesis when the null hypothesis is false. This is why we never say; we accept the null hypothesis but instead, we fail to reject. This language incorporates the uncertainty of hypothesis testing. The terminology might be tricky. I’ve used terms like confidence intervals here, but in the video, I refer to them as critical regions. You must be familiar with both. Check out the video for another look at these errors and for more tutorials on statistics, make sure to check out Actuarial Statistics on Udemy.
