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By X. Grok. Tabor College.

Descriptive Statistics Because relationships are never perfectly consistent buy 500mg tetracycline otc, researchers are usually confronted by many different scores that may have a relationship hidden in them purchase 250 mg tetracycline with visa. Descriptive statistics are proce- dures for organizing and summarizing sample data so that we can communicate and describe their important characteristics effective tetracycline 500mg. Thus cheap 250mg tetracycline with mastercard, for our study-time research buy tetracycline 250mg mastercard, we would use descriptive statistics to answer: What scores occurred? On the one hand, descriptive procedures are useful because they allow us to quickly and easily get a general understanding of the data without having to look at every single score. For example, hearing that the average error score for 1 hour of study is 12 simplifies a bunch of different scores. Likewise, you can summarize the overall relationship by men- tally envisioning a graph that shows data points that follow a downward slanting pattern. On the other hand, however, there is a cost to such summaries, because they will not precisely describe every score in the sample. A major goal of behavioral science is to be able to predict when a particular behavior will occur. This translates into predicting individuals’ scores on a variable that measures the behavior. To do this we use a relationship, because it tells us the high or low Y scores that tend to naturally occur with a particular X score. Then, by knowing someone’s X score and using the relationship, we can predict his or her Y score. Thus, from our previous data, if I know the number of hours you have studied, I can predict the errors you’ll make on the test, and I’ll be reasonably accurate. Inferential Statistics After answering the above questions for our sample, we want to answer the same ques- tions for the population being represented by the sample. Thus, although technically descriptive statistics are used to describe samples, their logic is also applied to popula- tions. Because we usually cannot measure the scores in the population, however, we must estimate the description of the population, based on the sample data. But remember, we cannot automatically assume that a sample is representative of the population. Therefore, before we draw any conclusions about the relationship in the population, we must first perform inferential statistics. Inferential statistics are proce- dures for deciding whether sample data accurately represent a particular relationship in the population. Essentially, inferential procedures are for deciding whether to believe what the sample data seem to indicate about the scores and relationship that would be found in the population. Thus, as the name implies, inferential procedures are for mak- ing inferences about the scores and relationship found in the population. If the sample is deemed representative, then we use the descriptive statistics com- puted from the sample as the basis for estimating the scores that would be found in the population. Thus, if our study-time data pass the inferential “test,” we will infer that a relationship similar to that in our sample would be found if we tested everyone after they had studied 1 hour, then tested everyone after studying 2 hours, and so on. Like- wise, we would predict that when people study for 1 hour, they will make around 12 errors and so on. Statistics versus Parameters Researchers use the following system so that we know when we are describing a sam- ple and when we are describing a population. A number that is the answer from a de- scriptive procedure (describing a sample of scores) is called a statistic. On the other hand, a number that describes a charac- teristic of a population of scores is called a parameter. Thus, for example, the average in your statistics class is a sample average, a descrip- tive statistic that is symbolized by a letter from the English alphabet. If we then esti- mate the average in the population, we are estimating a parameter, and the symbol for a population average is a letter from the Greek alphabet. Inferential proce- dures are for estimating parameters, which describe a population of scores and are symbolized using the Greek alphabet. Although we discuss a number of descriptive and inferential procedures, only a few of them are appropriate for a particular study. First, your choice depends on what it is you want to know—what question about the scores do you want to answer? A study’s design is the way the study is laid out: how many samples there are, how the partici- pants are tested, and the other specifics of how a researcher goes about demonstrating a relationship.

Recognize that a percent is a whole unit: Think of 50% as 50 of those things called percents order 250mg tetracycline visa. Creating Graphs One type of statistical procedure is none other than plotting graphs tetracycline 250 mg line. In case it’s been a long time since you’ve drawn one generic 500mg tetracycline otc, recall that the horizontal line across the bottom of a graph is the X axis order tetracycline 250mg fast delivery, and the vertical line at the left-hand side is the Y axis 250mg tetracycline with visa. Notice that because the lowest height score is 63, the lowest label on the X axis is also 63. We do this with either axis when there is a large gap between 0 and the lowest score we are plotting. Jane is 63 inches tall and weighs 130 pounds, so we place a dot above the height of 63 and opposite the weight of 130. Notice that you read the graph by using the scores on one axis and the data points. For example, to find the weight of the person who has a height of 67, travel vertically from 67 to the data point and then horizontally to the Y axis: 165 is the corresponding weight. In later chapters you will learn when to connect the data points with lines and when to create other types of figures. Regardless of the final form of a graph, always label the X and Y axes to indicate what the scores measure (not just X and Y), and always give your graph a title indicating what it describes. When creating a graph, make the spacing between the labels for the scores on an axis reflect the spacing between the actual scores. For example, the labels 10, 20, and 40 would not be equally spaced because the distance between these scores is not equal. Sometimes there are so many different scores that we cannot include a label for each one. Be careful here, because the units used in labeling each axis then determine the impression the graph gives. Say that for the previous weight scores, instead of labeling the Y axis in units of 10 pounds, we labeled it in units of 100 pounds, as shown in Figure 1. Thus, always label the axes in a way that honestly presents the data, without exaggerating or minimizing the pattern formed by the data points. If you compute your grade average or if you ask your instructor to “curve” your grades, you are using statistics. When you understand from the nightly news that Senator Fluster is projected to win the election or when you learn from a television commercial that Brand X “significantly” reduces tooth decay, you are using statistics. You simply do not yet know the formal names for these statistics or the logic behind them. All empirical research is based on observation and measurement, resulting in numbers, or scores. Statistical procedures are used to make sense out of data: They are used to organize, summarize, and communicate data and to draw conclusions about what the data indicate. The goal in learning statistics is to know when to perform a particular procedure and how to interpret the answer. Unless otherwise indicated, the order of mathematical operations is to compute inside parentheses first, then square or find square roots, then multiply or divide, and then add or subtract. Round off the final answer in a calculation to two more decimal places than are in the original scores. If the digit in the next decimal place is equal to or greater than 5, round up; if the digit is less than 5, round down. A transformation is a procedure for systematically converting one set of scores into a different set of scores. Transformations make scores easier to work with and make different kinds of scores comparable. To determine the score that produces a particular proportion, multiply the proportion times the total. To transform an original score to a percent, find the proportion by dividing the score by the total and then multiplying by 100. To find the original score that corresponds to a particular percent, transform the percent to a proportion and then multiply the proportion times the total. If given no other information, what is the order in which to perform mathematical operations? For each of the following, to how many places will you round off your final answer?

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