Statistics By Jim

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distributions

T Distribution: Definition & Uses

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What is the T Distribution?

The t distribution is a continuous probability distribution that is symmetric and bell-shaped like the normal distribution but with a shorter peak and thicker tails. It was designed to factor in the greater uncertainty associated with small sample sizes.

The t distribution describes the variability of the distances between sample means and the population mean when the population standard deviation is unknown and the data approximately follow the normal distribution. This distribution has only one parameter, the degrees of freedom, based on (but not equal to) the sample size. [Read more…] about T Distribution: Definition & Uses

Difference Between Standard Deviation and Standard Error

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The difference between a standard deviation and a standard error can seem murky. Let’s clear that up in this post!

Standard deviation (SD) and standard error (SE) both measure variability. High values of either statistic indicate more dispersion. However, that’s where the similarities end. The standard deviation is not the same as the standard error. [Read more…] about Difference Between Standard Deviation and Standard Error

Beta Distribution: Uses, Parameters & Examples

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The beta distribution is a continuous probability distribution that models random variables with values falling inside a finite interval. Use it to model subject areas with both an upper and lower bound for possible values. Analysts commonly use it to model the time to complete a task, the distribution of order statistics, and the prior distribution for binomial proportions in Bayesian analysis. [Read more…] about Beta Distribution: Uses, Parameters & Examples

Geometric Distribution: Uses, Calculator & Formula

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What is a Geometric Distribution?

The geometric distribution is a discrete probability distribution that calculates the probability of the first success occurring during a specific trial. In other words, during a series of attempts, what is the probability of success first occurring during each attempt? Use this distribution when you need to understand how many attempts are necessary to produce the first successful outcome. [Read more…] about Geometric Distribution: Uses, Calculator & Formula

Conditional Distribution: Definition & Finding

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What is a Conditional Distribution?

A conditional distribution is a distribution of values for one variable that exists when you specify the values of other variables. This type of distribution allows you to assess the dispersal of your variable of interest under specific conditions, hence the name. [Read more…] about Conditional Distribution: Definition & Finding

Marginal Distribution: Definition & Finding

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What is a Marginal Distribution?

A marginal distribution is a distribution of values for one variable that ignores a more extensive set of related variables in a dataset.

That definition sounds a bit convoluted, but the concept is simple. The idea is that when you have a larger set of related variables that you collected for a study, you might want to focus on one of them to answer a specific question. [Read more…] about Marginal Distribution: Definition & Finding

Cumulative Frequency: Finding & Interpreting

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What is Cumulative Frequency?

Cumulative frequency is the running total of frequencies in a table. Use cumulative frequencies to answer questions about how often a characteristic occurs above or below a particular value. It is also known as a cumulative frequency distribution.

For example, how many students are in the 4th grade or lower at a school? [Read more…] about Cumulative Frequency: Finding & Interpreting

Chi-Square Goodness of Fit Test: Uses & Examples

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What is the Chi Square Goodness of Fit Test?

The chi-square goodness of fit test evaluates whether proportions of categorical or discrete outcomes in a sample follow a population distribution with hypothesized proportions. In other words, when you draw a random sample, do the observed proportions follow the values that theory suggests. [Read more…] about Chi-Square Goodness of Fit Test: Uses & Examples

Kurtosis: Definition, Leptokurtic & Platykurtic

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What is Kurtosis?

Kurtosis is a statistic that measures the extent to which a distribution contains outliers. It assesses the propensity of a distribution to have extreme values within its tails. There are three kinds of kurtosis: leptokurtic, platykurtic, and mesokurtic. Statisticians define these types relative to the normal distribution. Higher kurtosis values indicate that the distribution has more outliers falling relatively far from the mean. Distributions with smaller values have a lower tendency for producing extreme values. When you’re assessing a sample, outliers have the greatest impact on this statistic. [Read more…] about Kurtosis: Definition, Leptokurtic & Platykurtic

Binomial Distribution: Uses & Calculator

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What is the Binomial Distribution?

The binomial distribution is a discrete probability distribution that calculates the likelihood an event will occur a specific number of times in a set number of opportunities. Use this distribution when you have a binomial random variable. These variables count how often an event occurs within a fixed number of trials. They have only two possible outcomes that are mutually exclusive. [Read more…] about Binomial Distribution: Uses & Calculator

Sampling Distribution: Definition, Formula & Examples

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What is a Sampling Distribution?

A sampling distribution of a statistic is a type of probability distribution created by drawing many random samples of a given size from the same population. These distributions help you understand how a sample statistic varies from sample to sample. [Read more…] about Sampling Distribution: Definition, Formula & Examples

Critical Value: Definition, Finding & Calculator

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What is a Critical Value?

A critical value defines regions in the sampling distribution of a test statistic. These values play a role in both hypothesis tests and confidence intervals. In hypothesis tests, critical values determine whether the results are statistically significant. For confidence intervals, they help calculate the upper and lower limits. [Read more…] about Critical Value: Definition, Finding & Calculator

5 Number Summary: Definition, Finding & Using

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What is the 5 Number Summary?

The 5 number summary is an exploratory data analysis tool that provides insight into the distribution of values for one variable. Collectively, this set of statistics describes where data values occur, their central tendency, variability, and the general shape of their distribution. [Read more…] about 5 Number Summary: Definition, Finding & Using