Design of experiments | Statistical hypothesis testing
In statistical hypothesis testing, a type I error is the mistaken rejection of an actually true null hypothesis (also known as a "false positive" finding or conclusion; example: "an innocent person is convicted"), while a type II error is the failure to reject a null hypothesis that is actually false (also known as a "false negative" finding or conclusion; example: "a guilty person is not convicted"). Much of statistical theory revolves around the minimization of one or both of these errors, though the complete elimination of either is a statistical impossibility if the outcome is not determined by a known, observable causal process.By selecting a low threshold (cut-off) value and modifying the alpha (α) level, the quality of the hypothesis test can be increased. The knowledge of type I errors and type II errors is widely used in medical science, biometrics and computer science. Intuitively, type I errors can be thought of as errors of commission, i.e. the researcher unluckily concludes that something is the fact. For instance, consider a study where researchers compare a drug with a placebo. If the patients who are given the drug get better than the patients given the placebo by chance, it may appear that the drug is effective, but in fact the conclusion is incorrect.In reverse, type II errors are errors of omission. In the example above, if the patients who got the drug did not get better at a higher rate than the ones who got the placebo, but this was a random fluke, that would be a type II error. The consequence of a type II error depends on the size and direction of the missed determination and the circumstances. An expensive cure for one in a million patients may be inconsequential even if it truly is a cure. (Wikipedia).
B05 Local truncation errors in numerical analysis
From playlist A Second Course in Differential Equations
Linear and quadratic approximations -- Calculus II
This lecture is on Calculus II. It follows Part II of the book Calculus Illustrated by Peter Saveliev. The text of the book can be found at http://calculus123.com.
From playlist Calculus II
Solve second order differential equation by substitution, Q10 on review sheet
Solve second order differential equation by substitution, 2nd order differential equation with variable coefficients, Differential equation by substitution, second order linear differential equations, blackpenredpen
From playlist First Order Differential Equations Review
B06 Example problem calculating the error
B06 Example problem calculating the error
From playlist A Second Course in Differential Equations
Find a Particular Solution to a Nonhomgeneous DE Using Variation of Parameters
This video explains how to determine a particular solution to a linear second order differential equation using the method of variation of parameters. http://mathispower4u.com
From playlist Linear Second Order Nonhomogeneous Differential Equations: Variation of Parameters
B22 Introduction to Substitutions
An overview of the three type of substitutions as a new method of solving linear, exact, and "almost" separable differential equations.
From playlist Differential Equations
Polynomial approximations -- Calculus II
This lecture is on Calculus II. It follows Part II of the book Calculus Illustrated by Peter Saveliev. The text of the book can be found at http://calculus123.com.
From playlist Calculus II
Type I and Type II error (Part IV of Intro to Statistics)
What are type I and type II errors in hypothesis tests? What they are, and ways to avoid them. 00:00 Intro 00:19 Definition of Type I and Type II Error 00:38 An example 00:56 Table of decision errors 04:4 Examples of Confidence Intervals and Type II Errors 08:12 Comparison of Errors with
From playlist Intro to Statistics
Type I and Type II Errors – Errors in Statistical Decision-making (7-10)
Whenever you make a decision, you could also make a mistake. This is true in life and in hypothesis testing. When you make a decision about whether or not to reject the null hypothesis, you could make a mistake. A Type I error is rejecting a null hypothesis that is actually “true” (a.k.a.
From playlist WK7 Sampling, Probability, & Inference - Online Statistics for the Flipped Classroom
Playing with Power: P-Values Pt 3: Crash Course Statistics #23
We're going to finish up our discussion of p-values by taking a closer look at how they can get it wrong, and what we can do to minimize those errors. We'll discuss Type 1 (when we think we've detected an effect, but there actually isn't one) and Type 2 (when there was an effect we didn't
From playlist Statistics
How To Identify Type I and Type II Errors In Statistics
This statistics video tutorial provides a basic introduction into Type I errors and Type II errors. A type I error occurs when a true null hypothesis is rejected. A type II error occurs when a false null hypothesis is not rejected. This video contains a few examples and practice problem
From playlist Statistics
A11 Eigenvalues with complex numbers
Eigenvalues which contain complex numbers.
From playlist A Second Course in Differential Equations
The double integral of two variables is an iterated integral. The outer integral should be between two constant if the answer is to be a number. In a type I region it is the x-values that are constants and make the bounds of the outer integral.
From playlist Advanced Calculus / Multivariable Calculus
Type I versus II error and power (FRM T2-13)
[My xls is here http://trtl.bz/2GldhxM] Type I error mistakenly rejects the true null. The Type II error mistakenly accepts a false null. Significance, α, is the desired Prob[Type I error]. Power is 1 - β = 1 - Prob[Type II error] but is more difficult to compute because, while there is on
From playlist Quantitative Analysis (FRM Topic 2)
Type I and Type II ERRORS in Hypothesis Testing (14-12)
Whenever you make a decision in hypothesis testing, you could make a mistake. The null hypothesis could be true, but you reject it; or, the null hypothesis could be false, but you “fail to reject” it. A Type I error is rejecting a null hypothesis that is actually true (false positive). A T
From playlist Hypothesis Testing Introduction WK 14 QBA 237
I recently uploaded 200 videos that are much more concise with excellent graphics. Click the link in the upper right-hand corner of this video. It will take you to my youtube channel where videos are arranged in playlists. In this older video: understanding Power and Type II Error and be
From playlist Older Statistics Videos and Other Math Videos
Examples identifying Type I and Type II errors | AP Statistics | Khan Academy
Examples identifying Type I and Type II errors. View more lessons or practice this subject at http://www.khanacademy.org/math/ap-statistics/tests-significance-ap/error-probabilities-power/v/examples-identifying-type-i-and-type-ii-errors?utm_source=youtube&utm_medium=desc&utm_campaign=apst
From playlist Significance tests (hypothesis testing) | AP Statistics | Khan Academy
Introduction to Type I and Type II errors | AP Statistics | Khan Academy
Introduction to Type I and Type II errors in significance testing. Significance levels as the probability of making a Type I error. View more lessons or practice this subject at http://www.khanacademy.org/math/ap-statistics/tests-significance-ap/error-probabilities-power/v/introduction-to
From playlist Significance tests (hypothesis testing) | AP Statistics | Khan Academy
Introduction to Hypothesis Testing Outcomes: Type I and Type II Errors
This video introduces the 4 outcomes of a hypothesis test.
From playlist Hypothesis Testing with One Sample
C33 Example problem using variation of parameters
Another example problem using the method of variation of parameters on second-order, linear, ordinary DE's.
From playlist Differential Equations