Regression – Part 2

In the previous post we saw how the size of the correlation between two variables affects the accuracy of prediction. We can see this reflected in the slope of the regression line when it is illustrated on a scatterplot. Take a look at this one: This plot is based on a positive correlation of r = .78. Notice how the regression line has some steepness to it. The stronger the…

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Regression – Part 1

Regression is a technique that we use when we want to predict something such as people’s opinions, attitudes, or even behaviors. Based on knowledge of one characteristic, we can predict with some accuracy another characteristic. How accurate our prediction is will depend on the strength of the relationship between the two characteristics, or variables. The stronger the relationship between the variables, the more accurate the prediction will be, and the…

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Correlation – Part 2

We know from the previous post that correlation gives us a number that tells us about the relationship between two variables (usually named X and Y). There are several types of correlation, but the most common one you’re likely to see discussed in research articles is Pearson’s r. The correlation coefficient that Pearson’s r produces is a ratio of how the variables vary together (their covariability) and how they vary…

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Correlation – Part 1

Correlation is a procedure that will tell us about the relationship between two variables. Specifically, it tells us about the nature of their covariability, or how they behave together. Are they related to each other? Is their relationship positive or negative? How strong or weak is their relationship? Correlation answers these questions for us. Suppose we are interested in whether students who sit and fret over a test do better…

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Percentile Ranks

In the previous post I described a percentile point as a score below which a certain percentage of the other scores in a data set lie. In finding a percentile point, we started with a desired percentage and found the corresponding score. Percentile ranks are similar in that we start with a score to find the corresponding percent. A percentile rank tells us the position of a score relative to…

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Percentile Points

Percentile points and ranks are used for comparison within a group, and are commonly used in education. For example, if your daughter comes home with her state exam grade for math showing she is at the 90th percentile for math, it means that she is scoring better than 90% of the others who took the same test. In other words, her percentile rank is 90%.  Percentile points give us similar…

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Standard Error of the Mean

The standard error of the meanis the average distance of all sample means from the population mean. In other words, if we could take the distance between each sample mean and the population mean, then get the average of all these distances, we would have the standard error of the mean. This is very similar to the standard deviation in a sample, which is the average distance the scores are…

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Central Limit Theorem

In the previous post we saw how it could be a problem to have no knowledge of the population mean when trying to decide whether a treated sample mean was significantly different from the population mean.  We also saw how the sampling distribution of the mean was the solution to this problem, but constructing one would usually be impossible.  But the central limit theorem makes it unnecessary anyway, and here…

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Sampling Distribution of the Mean

When we conduct research and gather data to analyze, we wind up with two things to compare: the mean of our treated sample and the mean of the population that has not been treated. For example, suppose we gather a sample from a population of people who never drink soda. Then, our sample of people is told to drink 5 sodas a day (known as the “treatment”) to see if…

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The Normal Distribution

Data is said to be normally distributed when it’s distribution, or occurrence of scores, follows the normal curve. It doesn’t have to be exactly perfect, but it should be approximately normal in order for us to use the typical statistical analyses that become necessary to answer research questions and/or address hypotheses. Why is this important? When performing statistical analyses, a common assumption is that the sample used to gather the…

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