Stats
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Accept-Reject SamplingStats 2022. 7. 14. 13:43
Sample and Sampling Sample A sample is an outcome of a random experiment. When we sample a random variable, we obtain one specific value out of the set of its possible values. That particular value is called a sample. The possible values and the likelihood of each are determined by the random variable's probability distribution. Sampling Mathematically performing sampling is the same as performi..
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Power and Effective sizeStats/Inferential 2020. 2. 5. 18:29
1. Overview 2. Description 2.1 Power ($1-\beta$) The probability of correctly rejecting a false null hypothesis $$Power=P(reject\: H_{0}|H_{1}\: is\: true)=1-\underbrace{P(not\: rejecting\: H_{0}|H_{0}\: false)}_{Type\: 2\: error}\\=1-\beta=P(not\: making\: Type\: 2\: error)$$ Particular Interpretation Sample Size Larger sample more power Effect Size Larger Effect sieze more power Alpha Level Hi..
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Lack-of-fit sum of squares and Pure-error sum of squaresStats/Inferential 2020. 2. 4. 12:17
1. Overview In statistics, a sum of squares due to lack of fit, or more tersely a lack-of-fit sum of squares, is one of the components of a partition of the sum of squares of residuals in an analysis of variance, used in the numerator in an F-test of the null hypothesis that says that a proposed model fits well. The other component is the pure-error sum of squares. 2. Description 2.1 Intuition $..
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Chi-squared DistributionStats/Distribution 2020. 1. 31. 15:21
1. Overview the chi-square distribution (also chi-squared or χ2-distribution) with k degrees of freedom is the distribution of a sum of the squares of k independent standard normal random variables. The chi-square distribution is a special case of the gamma distribution and is one of the most widely used probability distributions in inferential statistics, notably in hypothesis testing and in co..
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Type 1 Error and Type 2 ErrorStats/Inferential 2020. 1. 30. 14:22
1. Overview In statistical hypothesis testing, a type I error is the rejection of a true null hypothesis (also known as a "false positive" finding or conclusion), while a type II error is the non-rejection of a false null hypothesis (also known as a "false negative" finding or conclusion). 2. Description 2.1 Type 1 Error $\alpha$ It is often assimilated with false positives or Level of significa..
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Student's T distributionStats/Distribution 2020. 1. 16. 11:31
1. Overview Visually the Student's t distribution looks much like a normal distribution but generally has fatter tails. fatter tails allow for a higher dispersion of variables and there is more uncertainty. It is a small sample size approximation of a normal distribution. We use the Student's t distribution When it doesn't have sufficient data. Student's t distribution is frequently used when co..
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Confidence IntervalStats/Inferential 2020. 1. 16. 00:00
1. Overview 2. Description 2.1 Confidence Interval A confidence interval is a range within which you expect the population parameter to be and its estimation is based on the data we have in our sample. when our confidence is lower the confidence interval itself is smaller. Similarly, for a 99 percent confidence interval, we would have higher confidence but a much larger confidence interval that'..
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TerminologyStats 2020. 1. 15. 23:59
1. Overview 1.1 Estimate A specific value is called an estimate which is an approximation of population. 1.1.1 Point Estimates Single number 1.1.2 Confidence intervals Estimates A confidence interval naturally is an interval. In fact, the point estimate is located exactly in the middle of the confidence interval. However, confidence intervals provide much more information and are preferred when ..