Public Administration
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Chapter 12 introduces the reader to the true definition of statistics, without scaring them half to death. The book breaks statistics down in two parts: descriptive and inferential. The type that is dealt with in this chapter is descriptive statistics. The simple definition of descriptive statistics are that they are just numbers in different forms, for example, percentages, numerals, fractions, and decimals. The book gives an example of a grade point average being a descriptive statistic.
It is becoming increasingly important for classroom teachers to be able to understand and interpret statistics because of increasing calls for acountablity. Being able understand various types of statistics, there uses and limitations, will put the educator who does at an advantage. Instead of just averaging grades, there are important questions that every educator should want to know the answers to regarding their classroom. Questions like, how many people are above average and how many scored above the cutoff passing score, are questions that cant be answered without some working knowledge of statistics.
The bar graph explanation was pretty clear in the chapter, but that might be just because its the most frequently used graph to convey statistical data. Everyone is familiar with the bar graph, but when it comes down to frequency polygons things get a little fuzzy.
Chapter 13 explains how distributions can have the same values for the mode, median, and mean but are different in the way the scores are spread out. The variability estimate helps determine how compressed or expanded the distributions are.
The range is the easiest way to estimate variability and its determined from subtracting the lowest score from the highest score. In the case of the range, things can get thrown off if an extreme score is present. One way of preventing this from happening is to use the semi-interquartile range. This score is determined by taking the middle 50% of the scores in a distribution. The upper 25% and the lower 25% are not entered into its final computation.
Standard deviation is an estimate of variability that accompanies the mean in describing a distribution. You are taking a look at each distribution to see how far away each score deviates from the mean.
The normal distribution is a type of symmetrical distribution that is mathematically determined and has fixed properties. It is basically used as a model to base statistical decisions. These are methods that can most definitely be used in the classroom when analyzing data. After going over normal distribution the book gets into z scores a nd t scores. Im not sure about how much these concepts will actually get put to use in a classroom.
Chapter 14 covers the last statistsical topic in the book, correlation. Correlation is the concept of seeing if two things none related are in fact related, not to confuse that with causation. In this case we are looking at two different distributions of scores and if they correlate. Do left handed persons make better grades than right handed persons? Do students who make high marks in elementary school do better in high school? These are examples of questions that can be answered by using the correlation coefficient.
Distributions can correlate positively or negatively, and even not correlate at all. When high scores in distribution A are associated with high scores in distribution B or the same with low scores, there is a positive correlation. When high scores in distribution A are associated with low scores in distribution B or low scores in distribution A are associated with high scores in distribution B, there is a negative correlation.
Just because two things correlate does not mean that one of those variables actually caused the other. A correlation only shows that some kind of relationship exists between the two distributions. Usually the two variables correlated because of a third variable which is unidentified.
Chapter 15 deals with validity as it applies to testing. Does the test accurately measure what it says it measures? There are different ways to determine whether a test has sufficient validity evidence. The first way the book discusses is content validity which is also the simplest. Content validity is done by examining the test to see if they go along with what the user has decided should be covered on the test. As long as the test matches the instructional objectives it appears to “look” valid, but it doesnt tell whether the reading level is too high on the test or whether the questions are written poorly.
The second type of validity evidence is criterion related, its established when scores from a test are correlated with an external criterion. The two types are concurrent and predictive. Predictive validity evidence refers to how well the test predicts some future behavior of the examinee.
A test should measure what its supposed to measure. I have realized after this chapter that even though the tests I was giving to my students were made by the authors of the textbooks, they were not the most valid because some of the things I was emphasizing in the text were a lot of times not reflected on the tests given. I now know that I cant expect the results of the tests to be what they should if the tests are not valid.
Chapter 16 is about how reliability, consistency of rankings over time, affects testing. The book covers three ways to estimate the reliability of a test. The three basic methods used the most are called test-retest, alternate form, and internal consistency.
Test-retest is simply giving the same test twice and finding out the correlation between the first set of scores and the second set of scores. Alternate forms or equivalence method is used when there are two equivalent forms of a test. They are both administered to a group of students, and correlations between the two sets of scores are determined. If there are large differences between the two sets of tests that supposedly measure the same thing, the test is unreliable. Internal consistency is used when only one basic concept is being measured. The test is then split into halves and then determining the correlation between the two.
I understand now that if tests are not reliable, you end up getting results that are not accurate. Making decisions and judgments