chapter one introduction to statistics. copyright © houghton mifflin company. all rights...
TRANSCRIPT
Chapter One
Introduction to Statistics
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Some Commonly AskedQuestions about Statistics
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What Are Statistics?
The word statistics refers to statistical
procedures and the answers obtained
from those procedures.
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What Do Researchers Do with Statistics?
• Statistical procedures are used to– Organize,– Summarize, and– Communicate data
• Then to– Conclude what the data indicate
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What Is Empirical Research?
• Empirical means knowledge obtained through observation of events. Empirical research involves measurement.
• The scores obtained in research are the data.
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How Do I Learn Statistics?
More than anything else, you need to
learn when to use each statistical
procedure, why each statistical procedure
is used, and how to interpret its answer.
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Basic Statistical Notation
Statistical notation is the standardized
code for symbolizing the mathematical
operations performed in the formulas and
the answers we obtain.
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Review of MathematicsUsed in Statistics
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X
Mathematical Operations
• X or Y stand for each individual score obtained in a study.– Addition X + Y.– Subtraction X – Y.– Division X / Y.– Multiplication XY, (X)Y, or X(Y).
• “X squared” or “X times X.• “the square root of X.”
2X
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Parentheses and square root signs indicate “the quantity” so always find the
quantities indicated by these symbols first.
The Order of Math Operations
• Unless otherwise indicated
– Square or take the square root.
– Multiply or divide.
– Add or subtract.
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Rounding
• Carry out calculations so that the final answer after rounding has two more decimal places than the original scores
• Do not round off at intermediate steps in a formula
• If the number in the next decimal place is 5 or greater than 5, round up
• If the number in the next decimal place is less than 5, round down
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Transformations
A transformation is a mathematical
procedure for systematically converting a
set of scores into a different set of scores.
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Proportions
• A proportion is a decimal number between 0 and 1 that indicates a fraction of the total
• To transform a number to a proportion, divide the number by the total
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Percents
• A percent (or percentage) is a proportion multiplied by 100
• To transform a percent back into a proportion, divide the percent by 100
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Creating Graphs
• The horizontal line across the bottom of a graph is the X axis
• The vertical line at the left-hand side is the Y axis
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Plot of Height and Weight Scores