Tag Archives: z-score

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: Z-score Basics

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Z-Score Introduction

Standardized Distributions

Sometimes when working with data sets, we want to have the scores on the distribution standardized. Essentially, this means that we convert scores from a distribution so that they fit into a model that can be used to compare and contrast distributions from different works. For example, if you have a distribution of scores that show the temperature each day over the summer in Boston, it may be recorded in Fahrenheit. Someone else in Paris may have recorded their summer temperatures as well but in Celcius. If we wanted to compare these distributions of scores based on their descriptive statistics, we may want to convert them to the same standardized unit of measurement. 

Standardized distributions have one single unit of measurement. Raw scores are transformed into this standardized unit of measurement to be compared to one another. Ultimately, they should look just like the original distribution, the only difference is that the scores have been placed on a different unit of measurement. Continue reading →