lecture 1 - Descriptive Statistics Everything dealing with...

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Descriptive Statistics
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Everything dealing with collection, processing, analyzing, and interpretation of numerical data belongs to the domain of statistics . Statistics as a science develops statistical ideas from its probabilistic foundation, and applies them in the different fields of science and practice.
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Once the data have been obtained, we may organize and summarize them in such a way as to arrive at their orderly presentation. Such procedures are often termed descriptive statistics. For example, tabulation might be made of the heights of all university students, indicating an average height for each age.
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However, we may want to make some generalizations from these data. We may wish to conclude whether university males are on average taller than females. The ability to make such generalized conclusions, inferring characteristics of the whole from characteristics of its parts, lies within the realm of inferential statistics or inductive statistics.
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Types of Data and Variables Whenever we make an observation on a variable for some collection of individuals or objects, we call the results a data set . 1. Data on a Nominal (Categorical) Scale If we determine the car color for each of 5 cars and the results are grey, blue, red, brown, and black the collection of these 5 observations is a categorical or nominal data set . The order of listing the categories is irrelevant.
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2. Data on an Ordinal (Rank-order) Scale Numbers represent rank-orders , and do not give information regarding the differences between adjacent ranks. The characteristics can be put into categories but the categories can also be ordered. E.g., patient condition (good, fair, serious, critical), attitude scale (1=Strongly agree, 2=Agree, 3=Neutral, 4=Disagree, 5=Strongly disagree). Ordinal variables can order categories, but distances between categories are unknown.
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3. Data on an Interval Scale When objects or events can be distinguished from one another and ranked, and when the differences between measurements also have meaning, the interval scale of measurement is applicable. An interval variable is one that does have numerical distances between any two values. In a Fahrenheit thermometer, mercury rises in equal intervals called degrees.
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However, the zero point is arbitrary, chosen simply because Fahrenheit decided that the zero point on his scale would be 32° below the freezing point of water. Because the units are in equal intervals, it is possible to add and subtract across an interval scale. You can say that 100°F is 50° warmer than 50°F, but you cannot say that 100°F is twice as hot as 50°F because zero does not represent the complete absence of heat.
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4. Data on a Ratio Scale The zero point for these variables is not arbitrary but determined by nature so it is possible to multiply and divide across a ratio scale.
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