Posts tagged probability and statistics
All about the sampling distribution of the sample mean

Consider the fact though that pulling one sample from a population could produce a statistic that isn’t a good estimator of the corresponding population parameter. To correct for this, instead of taking just one sample from the population, we’ll take lots and lots of samples, and create a sampling distribution of the sample mean.

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Discrete probability distributions for discrete random variables

discrete random variable is a variable that can only take on discrete values. For example, if you flip a coin twice, you can only get heads zero times, one time, or two times; you can’t get heads 1.5 times, or 0.31 times.

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Calculating test statistics for means and proportions for one- and two-tailed tests

With any hypothesis test, we need to state the null and alternative hypotheses, then determine the level of significance. We’ve already covered these first two steps, and now we want to learn how to calculate the test statistic, which will depend on whether we’re running a two-tail test or a one-tail test.

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How changes to the data change the mean, median, mode, range, and IQR

In this lesson, we want to see what happens to our measures of central tendency and spread when we make changes to our data set. Specifically the changes made either by changing all the values in the set at once, or by adding a single data point to, or removing a single data point from, the data set.

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Two-way data compared to one-way data

Sometimes we talk about two-way data in terms of independent variables and dependent variables. In the case of one-way data, we had one independent variable, called the individuals, and one or more dependent variables, called the variables. In the case of two-way data, we have two independent categories on which the variables are dependent.

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Changing histograms into polygons, then into density curves

relative frequency histogram is the same as a regular histogram, except that we display the frequency of each category as a percentage of the total of the data. A frequency polygon is a polygon-shaped figure that shows the frequency at which each category occurs in the data set.

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Bernoulli random variables and mean, variance, and standard deviation

A Bernoulli random variable is a special category of binomial random variables. Specifically, with a Bernoulli random variable, we have exactly one trial only (binomial random variables can have multiple trials), and we define “success” as a 1 and “failure” as a 0.

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Type I and II errors and significance level

Type I error rate is the rejecting the null hypothesis when it’s true, and Type II error rate is the probability of accepting the null hypothesis when it’s false. Type I error is called “alpha,” and Type II error is called “beta.”

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