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§ 13.4 - 14.1 Terminology, Clinical Studies, Graphical Representations of Data. Terminology. A statistic is a piece of numerical information taken from a sample. A parameter is a piece of numerical information about the population being studied.

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## § 13.4 - 14.1 Terminology, Clinical Studies, Graphical Representations of Data

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**§ 13.4 - 14.1 Terminology, Clinical Studies, Graphical**Representations of Data**Terminology**• A statistic is a piece of numerical information taken from a sample. • A parameter is a piece of numerical information about the population being studied. • In other words, a statistic is an estimate for a parameter.**Terminology**• Sampling error is the difference between a parameter and the statistic used to estimate it. The causes of this error are:1. Error due to chance or sampling variability.2. A poorly chosen sample--sample bias. • If we have a sample of size n from a population of size N then the sampling rate is the ratio n/N.**The Capture-Recapture Method**• Step 1: Capture (choose) a sample of size n1 and tag a certain number of the animals/objects/people. • Step 2: After some amount of time, capture a new sample of size n2and take a count of the tagged individuals. Call this number k. • If the second sample is representative then the size of the population is N (n1)(n2)/k**Example: The N - value of the Monarch Butterfly**• Suppose 150 monarchs are caught, tagged and released. • A few days later 200 more monarchs are caught, of which only 2 are found to be tagged. • Estimate the N - value of the local monarch population.**Clinical Studies**• Clinical studies are concerned with determining whether a single variable is causes a certain effect. • The goal is to limit confounding variables--other possible causes. • In a controlled study the subjects are divided into two groups: the treatmentgroup and the control group. • If the subjects are assigned to the two groups randomly then the study is a randomized controlled study.**Clinical Studies**• If the control group is given a placebo then the study is a controlled placebo study. • If neither group of subjects knows whether they are receiving treatment or a placebo then the study is said to be blind. • If neither the subjects nor the scientists know who is receiving treatment and who is receiving a placebo then the study is referred to as double-blind.**48**40 32 44 72 64 44 28 72 36 44 36 44 44 44 96 72 44 32 72 36 40 76 36 32 40 40 24 36 32 76 72 44 48 40 32 60 72 72 28 48 44 40 72 40 48 36 36 48 36 44 76 44 40 40 40 40 40 40 32 44 48 36 76 60 40 48 36 56 44 4 40 48 48 40 Graphical Representations of Data • A data set is a collection of individual data points. Below is a data set consisting of test scores:**Score**4 24 28 32 36 40 44 48 56 60 64 72 76 96 Frequency 1 1 2 6 10 16 13 9 1 2 1 8 4 1 Frequency Table • One way we might summarize the data is in the form of a Frequency Table. • The number below each exam score is the number of students getting that score.**Bar Graphs**• Another convenient way to summarize the test scores is in the form of a bar graph:**Variables:Quantitative v. Qualitative**• A variable is any value or characteristic that varies with members of a population. • In the previous example, test scores would be considered a variable. • A variable is said to be quantitative if it represents a measurable quantity. • A variable that cannot be measured is called qualitative.**Variables:Continuous v. Discrete**• If the possible values of a variable are ‘countable’--or if there is some smallest increment we can use--the variable is said to be discrete. • If the difference between values of a variable can be arbitrarily small, then the variable is called continuous.**O**O A B A O A A A O B O B O O A O O A A A A AB A B A A O O A O O A A A O A O O AB Example: Blood Types Forty people recently donated blood and their types are listed below:**Example: Blood Types**While this data is qualitative, it is still possible to make both a frequency table and a bar graph to represent it:**Example: Blood Types**Another way to present the information is in the form of a pie chart. • What differentiates this from the previous tables and graphs is that it shows the percentage, or relative frequency of each blood type in the sample.**Let’s return for a moment to our test score example. . .**• Suppose the instructor decided to allocate grades as follows: A 80 - 100 B 50 - 79 C 30 - 49 D 0 - 29 • This is an example of using what are called class intervals • When there are too many different values or categories to display our data nicely, we will use these kinds of intervals to simplify the situation.**The test scores, when sorted into class intervals (in this**case the letter grades), can be graphed like this:**Histograms**• You may have noticed that in all the cases where we have given a chart or graph that the variable used was discrete. • How can we graphically display continuous variables? • We can use a variation on the bar graph called a histogram.**Age Interval***# of Grooms 20 - 25 11,768 25 - 30 9,796 30 - 35 3,300 35 - 40 840 40 - 45 404 45 - 50 83 Example: Age at first marriage. Based on a survey, the frequency table below was obtained for the age of groom at first marriage in the state of Wisconsin Using class intervals of length 10 (years) draw a histogram for the given data.**Age Interval***# of Grooms 20 - 25 11,768 25 - 30 9,796 30 - 35 3,300 35 - 40 840 40 - 45 404 45 - 50 83 Example: Age at first marriage. Based on a survey, the frequency table below was obtained for the age of groom at first marriage in the state of Wisconsin Using class intervals of length 10 (years) draw a histogram for the given data.**Age Interval***# of Grooms 20 - 25 11,768 25 - 30 9,796 30 - 35 3,300 35 - 40 840 40 - 45 404 45 - 50 83 Example: Age at first marriage. Now draw a histogram with intervals which are five years in length.**Age Interval***# of Grooms 20 - 25 11,768 25 - 30 9,796 30 - 35 3,300 35 - 40 840 40 - 45 404 45 - 50 83 Example: Age at first marriage. Now draw a histogram with intervals which are five years in length.

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