ed psych 613 statistics 1 course overview. what am i doing here? research is a part of our everyday...
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Ed Psych 613
Statistics 1
Course Overview
WHAT AM I DOING HERE? Research is a part of our everyday lives. In order to be able to conduct research
(master’s thesis doctoral dissertation), we must be able to understand statistics.
Even if we just want to be able to understand the research that affects our work, that we see in the media, or just the probability that it will rain tomorrow, we have to understand statistics.
DJ’s Guide to Statistics What frightens you??
2X
DJ’s Guide to Statistics What’s the solution?
Important Info Dr. D.J. Hendricks
231 Walnut St., Morgantown, WV 26505
304-293-6560 (W) 304-216-2033 (C) E-mail: [email protected] or
[email protected] Website:
http://www.jan.wvu.edu/djhstats
What You Need Textbook:
Statistics for the Behavioral Sciences, 7th Ed. by Gravetter and Wallnau.
Also Required: SPSS Version 16.0 Student Version Basic Hand Calculator—You will need to
know how to use your calculator.
How I Grade You will be graded on:
Mid-term test = 200 pts. Final Exam = 300 pts.
Grades assigned based on: A = 450 – 500 pts. B = 400 – 449 pts. C = 350 – 399 pts.
Stress Reduction Practice Homework will not be graded. Just after the next class, the homework
answers for the previous lesson will be put on the website.
Do your homework before the next class! Check your answers with the website!!
Lesson 1
Introduction and Basic Concepts
Chapter 1
Introduction to Statistics
Statistics are:
A set of methods and rules for organizing, summarizing, and interpreting information.
Data
Data are measurements or observations. A data set is a collection of
measurements or observations. A score is a single measurement or
observation. It also is called a raw score.
Populations and Samples
The population is the set of all individuals (events) of interest in a particular study.
Populations and Samples
A sample is a set of individuals (events) selected from a population and is intended to represent the population in a research study.
A sample usually is obtained through random selection.
Two Forms of Statistics Descriptive statistics
summarize, organize, and simplify
data from a population or a sample.
Two Forms of Statistics Inferential statistics use samples to
make generalizations about the population.
Parameter
A parameter is a value, usually a numerical value, that describes a population.
Remember: Population Parameter
Statistic
A statistic is a value, usually a numerical value, that describes a sample.
Remember: Sample Statistic
Sampling Error
…is the discrepancy, or amount of error, that exists between a sample statistic and the corresponding population parameter.
Variables and Constants A constant is a characteristic or
condition that does not vary, but is the same for every individual or measurement.
Variables and Constants A variable is a characteristic or condition
that changes or has different values for different individuals or measurements.
Scales of Measurement Nominal Ordinal Interval Ratio
The word “NOIR” means black in French.
Scales of Measurement
A nominal scale consists of a set of categories that have different names. Measurements label and categorize observations, but do not make any quantitative distinctions between observations.
Scales of Measurement On ordinal scale consists of a set of
categories that are organized in an ordered sequence. Measurements on an ordinal scale rank observations in terms of size or magnitude.
Scales of Measurement
An interval scale consists of ordered categories where all of the categories are intervals of exactly the same size.
Equal differences between numbers on the scale reflect equal differences in magnitude.
Ratios of magnitudes are not meaningful.
Scales of Measurement
A ratio scale is an interval scale with the additional feature of an absolute zero point.
Numbers do reflect ratios of magnitude. There is a true zero.
Its All Greek to Me! In statistics, we often use Greek letters
as symbols. Specifically, we use
Greek letters to indicate a population parameter
Latin (regular) letters to indicate a sample statistic.
Its All Greek to Me!
Parameters and their statistics indicates a population mean. indicates a sample mean.
indicates a population standard deviation.
indicates a sample standard deviation.
X
s
Its All Greek to Me! In statistics, we use the upper case
Greek letter Sigma
to stand for “sum.” It means to add all the scores for a given variable.
Mathematical Rules Do what is inside the parentheses FIRST! Adding a negative number is the same as
subtraction. Squaring a negative number yields a
positive number. Multiplying a positive by a negative yields a
negative, BUT multiplying two negatives yields a positive.
Exercise 1 Designed to introduce you to statistical
symbols and to build skills using the summation symbol.
Chapter 2
Frequency Distribution Tables
and Histograms
Frequency Distributions
Spelling test scores
3 33 45 22 31 54 33 21 43 2
4
Exercise 2
Designed to start you thinking about ways in which you might organize, summarize, and interpret a data set.
3 33 45 22 31 54 33 21 43 2
4
Frequency Distributions
A Frequency Distribution Table can help us summarize, describe, and understand this data.
3 33 45 22 31 54 33 21 43 2
4
Frequency DistributionsHelpful Hints—
Put data in order before constructing frequency distribution tables or histograms.
0 (zero) is a valid data value!
1 31 32 32 32 42 43 43 43 5
5
Frequency Distributions
Construct a table that includes the full range of observed values.
54321
Frequency Distributions
The frequency ( f ) is the number of times each score occurs in the data set.
X f5 24 43 72 41 2
Frequency Distributions
This is called a frequency distribution table.
X f5 24 43 72 41 2
N=19
Frequency Distributions
N is the total number of observations in the data set.
It is calculated by summing the frequency ( f ) column.
X f5 24 43 72 41 2
N=19
Frequency Distributions
The p column represents the proportion.
Divide the f value for each score (X) by N.
Ex: 2 / 19 = .105
X f p5 2 0.1054 4 0.2113 7 0.3682 4 0.2111 2 0.105
N=19 1.00
Frequency DistributionsThe percent (%) is calculated by multiplying the p column by 100.
X f p %5 2 0.105 10.54 4 0.211 21.13 7 0.368 36.82 4 0.211 21.11 2 0.105 10.5
N=19 1.00 100.0
Frequency DistributionsThe cumulative frequency (cf ) is the frequency of all scores at or below a given score.
Frequency DistributionThe cumulative percent (c%) is the percentage of all scores at or below a given score.
Frequency Distributions
Finding X from a Frequency Distribution Table.
X f fX5 2 5 x 2 = 104 4 4 x 4 = 163 7 3 x 7 = 212 4 2 x 4 = 81 2 1 x 2 = 2
X =57
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Symmetrical
Fre
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Frequency Distributions
What would you do with these data?
30 51 67 3823 33 27 4858 18 42 3628 33 46 3135 25 35 39
Frequency Distributions
Using bins makes arranging this data much easier.
X60-6950-5940-4930-3920-2910-19
Frequency Distributions
Grouped Frequency Distribution Table
X f p %60-69 1 0.05 5%50-59 2 0.10 10%40-49 3 0.15 15%30-39 9 0.45 45%20-29 4 0.20 20%10-19 1 0.05 5%
Frequency Distributions
Use the frequency distribution table to construct a frequency distribution histogram!
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Number of Correct Answers (Scores)
Fre
qu
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X f5 24 43 72 41 2
N=19
Frequency Distributions Frequency distributions can be symmetrical.
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Symmetrical
Fre
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Frequency Distributions
Frequency distributions can be positively skewed.
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Positively Skewed
Fre
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Frequency Distributions
Frequency distributions can be negatively skewed.
012345678
1 2 3 4 5
Negatively Skewed
Fre
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Frequency Distributions
012345678
1 2 3 4 5
Negatively SkewedF
req
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Positively Skewed
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