Author Archives: Jason Green

Statistics: Sampling Distribution of the Proportion

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Sampling Distribution of the Proportion

In this section, we’ll be talking about finding the probability of a sample proportion. You may remember that a sampling distribution is a distribution not of scores, but all possible sample outcomes which can be drawn given that we’re working with a specific n. In this case, the following equations can help us figure out, based on a population proportion, how likely it is that we’ll draw a sample that has a chosen proportion. A question which would require these equations may sound like the following:

“A nation-wide survey was conducted about the perception of a brand. People were asked whether they liked the brand or disliked the brand and the results showed that 65% of people liked the brand. If we were to draw a random sample of 200 people, what is the probability that 80% of people within that sample will say they like the brand?”

The population proportion, denoted as ?, is the proportion of items in the entire population with the particular characteristic that we’re interested in investigating. The sample proportion, denoted by p, is the proportion of items in the sample with the characteristic that we’re interested in investigating. The sample proportion, which by definition is a statistic, is used to estimate the population proportion, which by definition is a parameter. Continue reading →

Statistics: Discrete Probability Distributions

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Introduction to Discrete Probability Distributions

Discrete versus Continuous Variables

A discrete variable typically originates from a counting process while a continuous variable usually comes from a measuring process. An easy way to make the distinction between a discrete and a continuous variable is that discrete variables are usually whole numbers with no decimals. Continuous variables on the other hand frequently take the form of decimals. For instance, the number of people which exist within a group is a discrete variable because it’s always a whole number, while a person’s weight would be continuous since it can typically be measured to multiple decimal places.

The Probability Distribution for a Discrete Variable

A probability distribution for a discrete variable is simply a compilation of all the range of possible outcomes and the probability associated with each possible outcome. Since, probability in general, by definition, must sum to 1, the summation of all the possible outcomes must sum to 1. For example, if you’re flipping a coin once, there’s a 1 in 2 chance it will land on heads, and a 1 in 2 chance it will land on tails; 1/2 + 1/2 = 1. In this way, measuring probability is similar to the use of percentages. Percentages are always measured out of 100 while probability is always measured out of 1. This is true for all probability measurements Continue reading →