Pearson Product-Moment Correlation - When you should run this test, the range of values the coefficient can take and how to measure strength of association. What does this test do? The Pearson product-moment correlation coefficient (or Pearson correlation coefficient, for short) is a measure of the strength of a linear association between two variables and is denoted by r. Basically, a Pearson product-moment correlation attempts to draw a line of best fit through the data of two variables, and the Pearson correlation coefficient, r, indicates how far away all these data points are to this line of best fit (i.e., how well the data points fit this new model/line of best fit).
What values can the Pearson correlation coefficient take? The Pearson correlation coefficient, r, can take a range of values from +1 to -1. A value of 0 indicates that there is no association between the two variables. How can we determine the strength of association based on the Pearson correlation coefficient? Are there guidelines to interpreting Pearson's correlation coefficient? Yes, the following guidelines have been proposed: How can you detect a linear relationship? Intro to Linear Regression. Stem-and-Leaf Plots. Stem-and-Leaf Plots (page 1 of 2) Stem-and-leaf plots are a method for showing the frequency with which certain classes of values occur.
You could make a frequency distribution table or a histogram for the values, or you can use a stem-and-leaf plot and let the numbers themselves to show pretty much the same information. For instance, suppose you have the following list of values: 12, 13, 21, 27, 33, 34, 35, 37, 40, 40, 41. You could make a frequency distribution table showing how many tens, twenties, thirties, and forties you have: You could make a histogram, which is a bar-graph showing the number of occurrences, with the classes being numbers in the tens, twenties, thirties, and forties: (The shading of the bars in a histogram isn't necessary, but it can be helpful by making the bars easier to see, especially if you can't use color to differentiate the bars.)
On the other hand, you could make a stem-and-leaf plot for the same data: That's pretty much all there is to a stem-and-leaf plot. Scatter Plots. Scatter plots are similar to line graphs in that they use horizontal and vertical axes to plot data points. However, they have a very specific purpose. Scatter plots show how much one variable is affected by another. The relationship between two variables is called their correlation . Scatter plots usually consist of a large body of data. The closer the data points come when plotted to making a straight line, the higher the correlation between the two variables, or the stronger the relationship. If the data points make a straight line going from the origin out to high x- and y-values, then the variables are said to have a positive correlation . A perfect positive correlation is given the value of 1.
An example of a situation where you might find a perfect positive correlation, as we have in the graph on the left above, would be when you compare the total amount of money spent on tickets at the movie theater with the number of people who go. Let's take a look at some examples. Reading and Interpreting Stem and Leaf Diagrams - Examples With Solutions. Tutorial on how to read and interpret stem and leaf diagrams. Example 1: The stem and leaf plot below shows the grade point averages of 18 students. The digit in the stem represents the ones and the digit in the leaf represents the tenths. So for example 0 | 8 = 0.8, 1 | 2 = 1.2 and so on. a) What is the range of the data in the stem and leaf plot?
B) How many students have a grade of 2 or more? C) What is the mode of the grades? D) What is the median of the grades? Solution to Example 1: a) range = maximum value - minimum value = 4.0 - 0.8 = 3.2 b) 7 + 4 + 1 = 12 students c) two modes: 1.4 and 2.5 d) There are 18 data values and already ordered in the stem and leaf diagram. median = (the 9th value + the 10th value) / 2 = (2.5 + 2.5) / 2 = 2.5 Example 2: The back to back stem and leaf plot below shows the exam grades (out of 100) of two sections. A) How many students scored higher than 60 in section 1? B) How many students scored higher than 60 in section 2? Solution to Example 2: e) section 1. HOTmaths: exploring measures of spread | EQUELLA. <h1>Error</h1><p class="error">This Web site requires JavaScript.
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Box Plots Lesson.