Analysis of Variance (ANOVA)

Basic Statistics

Bayes Rule

Benfords Law

Bernoulli Trials

Binomial Distribution

Chebyshevs Theorem

Chi-Square χ^{2} Test

Chi-Square Critical Values

Class Frequency Goodness of Fit

Coin Toss Probability

Confidence Interval for the Mean

Confidence Interval for Variance and Standard Deviation

Confidence Interval of a Proportion

Confidence Interval/Hypothesis Testing for the Difference of Means

Container Arrangements

Covariance and Correlation coefficient (r) and Least Squares Method and Exponential Fit

Critical Values for F-test

Critical Z-values

Difference of Proportions Test

Event Likelihood

Expected Frequency

Expected Value

Exponential Distribution

Exponential Smoothing

F Test Statistic

Favorable Outcome

Fisher Transformation and Fisher Inverse

Fishers Exact Test

Frequency Distribution Table

Fundamental Rule of Counting

Geometric Distribution

Grand Mean

Hypergeometric Distribution

Hypothesis Testing for a proportion

Hypothesis testing for the mean

MAPE - MPE - MAPD

Margin of Error from Confidence Interval

Mcnemar Test

Missing Average

Multinomial Distribution

Negative Binomial Distribution

Normal Distribution

Odds Probability

Odds Ratio

P-Hat Confidence Interval

Paired Means Difference

Percentile for Normal Distribution

Percentiles

Point Estimate and Margin of Error

Poisson Distribution

Probability

Probability (A U B U C)

Probability (A U B)

Proportion Sample Size

Random Sampling from the Normal Distribution

Random Test

Rule of Succession

Sample Size Reliability for μ

Sample Size Requirement for the Difference of Means

Sample Space Probability

Sign Test

Standard Normal Distribution

Student-t Distribution Critical Values

Tabular Display

Trimmed Mean and Winsorized Mean

Uniform Distribution

Venn Diagram (2 circles)

Z Score Lookup

Performs 1 way analysis of variance or 2 way analysis of variance on a set of data with critical value test and conclusion.

Calculator · Watch the VideoBasic Statistics

Given a number set, and an optional probability set, this calculates the following statistical items:

Expected Value

Mean = μ

Variance = σ^{2}

Standard Deviation = σ

Standard Error of the Mean

Skewness

Mid-Range

Average Deviation (Mean Absolute Deviation)

Median

Mode

Range

Pearsons Skewness Coefficients

Entropy

Upper Quartile (hinge) (75th Percentile)

Lower Quartile (hinge) (25th Percentile)

InnerQuartile Range

Inner Fences (Lower Inner Fence and Upper Inner Fence)

Outer Fences (Lower Outer Fence and Upper Outer Fence)

Suspect Outliers

Highly Suspect Outliers

Stem and Leaf Plot

Ranked Data Set

Central Tendency Items such as Harmonic Mean and Geometric Mean and Mid-Range

Root Mean Square

Weighted Average (Weighted Mean)

Frequency Distribution

Successive Ratio

Calculator · Watch the VideoExpected Value

Mean = μ

Variance = σ

Standard Deviation = σ

Standard Error of the Mean

Skewness

Mid-Range

Average Deviation (Mean Absolute Deviation)

Median

Mode

Range

Pearsons Skewness Coefficients

Entropy

Upper Quartile (hinge) (75th Percentile)

Lower Quartile (hinge) (25th Percentile)

InnerQuartile Range

Inner Fences (Lower Inner Fence and Upper Inner Fence)

Outer Fences (Lower Outer Fence and Upper Outer Fence)

Suspect Outliers

Highly Suspect Outliers

Stem and Leaf Plot

Ranked Data Set

Central Tendency Items such as Harmonic Mean and Geometric Mean and Mid-Range

Root Mean Square

Weighted Average (Weighted Mean)

Frequency Distribution

Successive Ratio

Bayes Rule

Calculates the conditional probabilities of (B given A) of 2 events and a conditional probability event using Bayes Rule

CalculatorBenfords Law

Shows you Benfords Law and evaluates a data set compared to Benfords Law

Calculator · Watch the VideoBernoulli Trials

Given a success probability p and a number of trials (n), this will simulate Bernoulli Trials and offer analysis using the Bernoulli Distribution. Also calculates the skewness, kurtosis, and entropy

Calculator · Watch the VideoBinomial Distribution

Calculates the probability of 3 separate events that follow a binomial distribution. It calculates the probability of exactly k successes, no more than k successes, and greater than k successes as well as the mean, variance, standard deviation, skewness and kurtosis.

Also calculates the normal approximation to the binomial distribution with and without the continuity correction factor

Calculates moment number t using the moment generating function

Calculator · Watch the VideoAlso calculates the normal approximation to the binomial distribution with and without the continuity correction factor

Calculates moment number t using the moment generating function

Chebyshevs Theorem

Using Chebyshevs Theorem, this calculates the following:

Probability that random variable X is within k standard deviations of the mean.

How many k standard deviations within the mean given a P(X) value.

Calculator · Watch the VideoProbability that random variable X is within k standard deviations of the mean.

How many k standard deviations within the mean given a P(X) value.

Chi-Square χ

This calculator determines a χ^{2} chi-square test on a test statistic and determines if it is outside an accepted range with critical value test and conclusion.

Calculator · Watch the VideoChi-Square Critical Values

Given a probability, this calculates the critical value for the right-tailed and left-tailed tests for the Chi-Square Distribution. CHIINV from Excel is used as well.

Calculator · Watch the VideoClass Frequency Goodness of Fit

Performs a goodness of fit test on a set of data with class boundaries (class boundary) with critical value test and conclusion.

CalculatorCoin Toss Probability

This calculator determines the following coin toss probability scenarios

* Coin Toss Sequence such as HTHHT

* Probability of x heads and y tails

* Probability of at least x heads in y coin tosses

* Probability of at least x tails in y coin tosses

* Probability of no more than x heads in y coin tosses

* Probability of no more than x tails in y coin tosses

* (n) Coin Tosses with a list of scenario results displayed

* Monte Carlo coin toss simulation

Calculator · Watch the Video* Coin Toss Sequence such as HTHHT

* Probability of x heads and y tails

* Probability of at least x heads in y coin tosses

* Probability of at least x tails in y coin tosses

* Probability of no more than x heads in y coin tosses

* Probability of no more than x tails in y coin tosses

* (n) Coin Tosses with a list of scenario results displayed

* Monte Carlo coin toss simulation

Confidence Interval for the Mean

Calculates a (90% - 99%) estimation of confidence interval for the mean given a small sample size using the student-t method with (n - 1) degrees of freedom or a large sample size using the normal distribution Z-score (z value) method including Standard Error of the Mean. confidence interval of the mean

Calculator · Watch the VideoConfidence Interval for Variance and Standard Deviation

Calculates a (95% - 99%) estimation of confidence interval for the standard deviation or variance using the χ^{2} method with (n - 1) degrees of freedom.

Calculator · Watch the VideoConfidence Interval of a Proportion

Given N, n, and a confidence percentage, this will calculate the estimation of confidence interval for the population proportion π including the margin of error. confidence interval of the population proportion

Calculator · Watch the VideoConfidence Interval/Hypothesis Testing for the Difference of Means

Given two large or two small distriutions, this will determine a (90-99)% estimation of confidence interval for the difference of means for small or large sample populations.

Also performs hypothesis testing including standard error calculation.

CalculatorAlso performs hypothesis testing including standard error calculation.

Container Arrangements

Given a set of items inside a container, this calculates the probability that you draw certain items in the following fashion:

Draw__all__ the items

Draw__any of__ the items

How many ways can you choose m items of a, n items of b, o items of c, etc.

CalculatorDraw

Draw

How many ways can you choose m items of a, n items of b, o items of c, etc.

Covariance and Correlation coefficient (r) and Least Squares Method and Exponential Fit

Given two distributions X and Y, this calculates the following:

* Covariance of X and Y denoted Cov(X,Y)

* The correlation coefficient r.

* Using the least squares method, this shows the least squares regression line (Linear Fit) and Confidence Intervals of α and Β (90% - 99%)

Exponential Fit

* Coefficient of Determination r squared r^{2}

* Spearmans rank correlation coefficient

* Wilcoxon Signed Rank test

Calculator · Watch the Video* Covariance of X and Y denoted Cov(X,Y)

* The correlation coefficient r.

* Using the least squares method, this shows the least squares regression line (Linear Fit) and Confidence Intervals of α and Β (90% - 99%)

Exponential Fit

* Coefficient of Determination r squared r

* Spearmans rank correlation coefficient

* Wilcoxon Signed Rank test

Critical Values for F-test

Calculate a critical value for the F-Test statistic based on DF1, DF2, and α

CalculatorCritical Z-values

Given a probability from a normal distribution, this will generate the z-score critical value. Uses the NORMSINV Excel function.

Calculator · Watch the VideoDifference of Proportions Test

Calculates a test statistic and conclusion for a hypothesis for the difference of proportions

CalculatorEvent Likelihood

Given a probability, this determines how likely that event is

CalculatorExpected Frequency

Given a contingency table (two-way table), this will calculate expected frequencies and then determine a conclusion based on a Χ^{2} test with critical value test and conclusion.

Calculator · Watch the VideoExpected Value

This lesson walks you through what expected value is, expected value notation, the expected value of a discrete random variable, the expected value of a continuous random variable, and expected value properties.

Lesson · Watch the VideoExponential Distribution

Calculates the Probability Density Function (PDF) and Cumulative Density Function (CDF) of the exponential distribution as well as the mean, variance, standard deviation, and entropy.

Calculator · Watch the VideoExponential Smoothing

Performs exponential smoothing on a set of data.

Calculator · Watch the VideoF Test Statistic

Calculates the F-test statistic for two populations

Calculator · Watch the VideoFavorable Outcome

Shows you various examples of favorable outcome in probability

Lesson · Watch the VideoFisher Transformation and Fisher Inverse

Given a correlation coefficient (r), this calculates the Fisher Transformation (z).

Given a Fisher Transformation (r), this calculates the Fisher Inverse (r)

Calculator · Watch the VideoGiven a Fisher Transformation (r), this calculates the Fisher Inverse (r)

Fishers Exact Test

Given a, b, c, and d, this calculates the probability of any such set of values using Fishers exact Test

Calculator · Watch the VideoFrequency Distribution Table

Determines the classes and frequency distribution using the 2 to k rule.

CalculatorFundamental Rule of Counting

Given a set of items, this calculates the total number of groups/choices that can be formed using the rule of product.

Calculator · Watch the VideoGeometric Distribution

Using a geometric distribution, it calculates the probability of exactly k successes, no more than k successes, and greater than k successes as well as the mean, variance, standard deviation, skewness, and kurtosis.

Calculates moment number t using the moment generating function

CalculatorCalculates moment number t using the moment generating function

Grand Mean

Calculates the grand mean of a set of number sets.

Calculator · Watch the VideoHypergeometric Distribution

Calculates the probability of drawing x objects out of a subgroup of k with n possibilities in a total group of N using the hypergeometric distribution.

Calculator · Watch the VideoHypothesis Testing for a proportion

Performs hypothesis testing using a test statistic for a proportion value.

CalculatorHypothesis testing for the mean

Performs hypothesis testing on the mean both one-tailed and two-tailed and derives a rejection region and conclusion

CalculatorMAPE - MPE - MAPD

Given a time series of actual and forecasted values, this determines the following:

* Mean Absolute Percentage Error (MAPE) also known as the Mean Absolute Percentage Deviation (MAPD)

* Symmetric Mean Absolute Percentage Error (sMAPE)

* Mean Absolute Percentage Error (MPE)

Calculator* Mean Absolute Percentage Error (MAPE) also known as the Mean Absolute Percentage Deviation (MAPD)

* Symmetric Mean Absolute Percentage Error (sMAPE)

* Mean Absolute Percentage Error (MPE)

Margin of Error from Confidence Interval

Given a confidence interval, this determines the margin of error and sample mean.

Calculator · Watch the VideoMcnemar Test

Given a 2 x 2 contingency table and a significance level, this will determine the test statistic, critical value, and hypothesis conclusion using a Mcnemar test.

CalculatorMissing Average

Given a set of scores and an average, this calculates the next score necessary to attain that average

Calculator · Watch the VideoMultinomial Distribution

Given a set of x_{i} counts and a respective set of probabilities θ_{i}, this calculates the probability of those events occurring.

Calculator · Watch the VideoNegative Binomial Distribution

Calculates the probability of the k^{th} success on the x^{th} try for a negative binomial distribution also known as the Pascal distribution.? ? It calculates the probability of exactly k successes, no more than k successes, and greater than k successes as well as the mean, variance, and standard deviation.

Calculator · Watch the VideoNormal Distribution

Calculates the probability that a random variable is less than or greater than a value or between 2 values using the Normal Distribution z-score (z value) method (Central Limit Theorem).

Also calculates the Range of values for the 68-95-99.7 rule, or three-sigma rule, or empirical rule. Calculates z score probability

CalculatorAlso calculates the Range of values for the 68-95-99.7 rule, or three-sigma rule, or empirical rule. Calculates z score probability

Odds Probability

Given an odds prediction m:n of an event success, this calculates the probability that the event will occur or *not* occur

Calculator · Watch the VideoOdds Ratio

This calculator determines the odds ratio for 2 groups X and Y with success and failure for an outcome.

Calculator · Watch the VideoP-Hat Confidence Interval

Given a large sized distribution, and a success amount for a certain criteria x, and a confidence percentage, this will calculate the confidence interval for that criteria.

CalculatorPaired Means Difference

Calculates an estimation of confidence interval for a small or large sample difference of data. Confidence interval for paired means

CalculatorPercentile for Normal Distribution

Given a mean, standard deviation, and a percentile range, this will calculate the percentile value.

CalculatorPercentiles

Given a set of scores and a target score, this will determine the percentile of the target score using two different formulas.

Calculator · Watch the VideoPoint Estimate and Margin of Error

Given an upper bound and a lower bound and a sample size, this calculate the point estimate, margin of error.

CalculatorPoisson Distribution

Calculates the probability of 3 separate events that follow a poisson distribution.

It calculates the probability of exactly k successes P(x = k)

No more than k successes P (x <= k)

Greater than k successes P(x >= k)

Each scenario also calculates the mean, variance, standard deviation, skewness, and kurtosis.

Calculates moment number t using the moment generating function

Calculator · Watch the VideoIt calculates the probability of exactly k successes P(x = k)

No more than k successes P (x <= k)

Greater than k successes P(x >= k)

Each scenario also calculates the mean, variance, standard deviation, skewness, and kurtosis.

Calculates moment number t using the moment generating function

Probability

This lesson walks you through the basics of probability like the probability definition, events, outcomes, experiments, and probability postulates

Lesson · Watch the VideoProbability (A U B U C)

Calculates the probability of a union of a three event sample space, A, B, and C, as well as P(A), P(B), P(C), P(A ∩ B), P(A ∩ C), P(B ∩ C), P(A ∩ B ∩ C).

CalculatorProbability (A U B)

Given a 2 event sample space A and B, this calculates the probability of the following events:

P(A U B)

P(A)

P(B)

P(A ∩ B)

CalculatorP(A U B)

P(A)

P(B)

P(A ∩ B)

Proportion Sample Size

This calculator determines a sample size to select to meet certain criteria related to a confidence percentage, reliability percentage, and a p value proportion. Simply enter your values not using percentage signs. This works whether p^ is known or not known.

Calculator · Watch the VideoRandom Sampling from the Normal Distribution

This performs hypothesis testing on a sample mean with critical value on a sample mean or calculates a probability that Z <= z or Z >= z using a random sample from a normal distribution.

CalculatorRandom Test

Given a set of data and an α value, this determines the test statistic and accept/reject hypothesis based on randomness of a dataset.

CalculatorRule of Succession

Given s successes in n independent trials, this calculates the probability that the next repetition is a success

Calculator · Watch the VideoSample Size Reliability for μ

Given a population standard deviation σ, a reliability (confidence) value or percentage, and a variation, this will calculate the sample size necessary to make that test valid.

Calculator · Watch the VideoSample Size Requirement for the Difference of Means

Given a population standard deviation 1 of σ_{1}, a population standard deviation 2 of σ_{2} a reliability (confidence) value or percentage, and a variation, this will calculate the sample size necessary to make that test valid.

CalculatorSample Space Probability

Given a sample space S and an Event Set E, this calculates the probability of the event set occuring.

Calculator · Watch the VideoSign Test

This will determine whether to accept or reject a null hypothesis based on a number set, mean value, alternative hypothesis, and a significance level using the Sign Test.

CalculatorStandard Normal Distribution

Givena normal distribution z-score critical value, this will generate the probability. Uses the NORMSDIST Excel function.

CalculatorStudent-t Distribution Critical Values

Given an α value and degrees of freedom, this calculates the right-tailed test and left-tailed test critical values for the Student-t Distribution

Calculator · Watch the VideoTabular Display

Enter a set of x and p(x) in a tabular probability distribution format and this will evaluate if it is valid or not.

Calculator · Watch the VideoTrimmed Mean and Winsorized Mean

Given a number set and a trimmed mean percentage, this will calculate the trimmed mean (truncated mean) or winsorized mean.

Calculator · Watch the VideoUniform Distribution

This calculates the following items for a uniform distribution

* Probability Density Function (PDF) ƒ(x)

* Cumulative Distribution Function (CDF) F(x)

* Mean, Variance, and Standard Deviation

Calculates moment number t using the moment generating function

Calculator · Watch the Video* Probability Density Function (PDF) ƒ(x)

* Cumulative Distribution Function (CDF) F(x)

* Mean, Variance, and Standard Deviation

Calculates moment number t using the moment generating function

Venn Diagram (2 circles)

Given two circles A and B with an intersection piece of C, this will calculate all relevant probabilities of the Venn Diagram.

CalculatorZ Score Lookup

Given a Z-score probability statement from the list below, this will determine the probability using the normal distribution z-table.

* P(z < a)

* P(z <= a)

* P(z > a)

* P(z >= a)

* P(a < z < b) Calculates z score probability

Calculator* P(z < a)

* P(z <= a)

* P(z > a)

* P(z >= a)

* P(a < z < b) Calculates z score probability