ped 471: height histogram spring 2001. introduction to statistics giving meaning to measurement...
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PED 471: Height HistogramPED 471: Height HistogramSpring 2001Spring 2001
Introduction to Introduction to StatisticsStatistics
Giving Meaning to Measurement
Chapter 4:94-104
If You Don’t Agree With If You Don’t Agree With Someone’s Conclusion…Someone’s Conclusion…
Determine if the data is accurate!
Determine if the logic makes sense! Was their
evaluation of the data appropriate?
Giving Meaning to Giving Meaning to MeasurementsMeasurements ACCURATE DATA: Depends
on good tests and qualified “testers”
GOOD LOGIC: Depends on appropriate evaluations of the assessments.
Test Validity Comes Later…Test Validity Comes Later…
First let’s take a look at “Evaluation”
How can statistics help us evaluate data?
Evaluate these scoresEvaluate these scoresBefore Supplement After
Sub 1. 10.3Sub 2. 9.8Sub 3. 11.7Sub 4. 13.2Sub 5. 9.9Sub 6. 11.0
Sub 1. 10.3Sub 2. 10.0Sub 3. 9.9Sub 4. 11.7Sub 5. 10.0Sub 6. 10.3
Can’t really conclude?Can’t really conclude?This is why we need systematic
means for data evaluation (Draw me a picture)
We need to condense the scores and look at the entire group
We then assign “rules” that will help us decide how to evaluate the data (or in research, make conclusions)
What Does What Does “Statistics” Do?“Statistics” Do?
*Describes sets of data
*Compares (For Evaluation) sets to other sets
*Making Conclusions (Inferences)
Types of Statistics
Descriptive: “describes” a set of scores – summary stats
Correlational: looking for Relationships
Inferential: Drawing conclusions
Basic Terminology:Basic Terminology:Constants: Qualities that never change
in a selected populationE.g. female students at WSC – Female is
constantVariables: Qualities expected to
change or vary within a population or between individuals:E.g. The GPA of female students at WSC
Types of ScoresTypes of ScoresNominal: Scores cannot be
ranked, and are mutually exclusive: ie. Gender, eye color, etc. - presence or absence of a quality (variable) is “named”
Ordinal: Ordering scores by “less than” or “more than” - relative amounts of that quality
The Most Common Types The Most Common Types of Scores in PE/ESof Scores in PE/ES Interval: A precise value with a UNIT of
measure: Inches, pounds, ml/kg/min, seconds
Ratio: A unit-less value given to a score which “builds in” a comparison:MET: 10 Mets is a ratio indicating VO2
is 10 times the resting metabolic rate of 3.5 ml/kg/min
Math Review
Know your symbols
Know “Order of Operations”
Know your calculator!
Assignment:
Compile Data: Height and Resting HR of 20
studentsComplete “Stat Problems #1”
(Math for Muscle Heads)
DATA EVALUATION:DATA EVALUATION:“Draw Me a Picture”“Draw Me a Picture”
Organizing the Data
Tables: Ordering the dataPictures: (Histograms)
Seeing a pattern in the dataFormulas: Trusting your
eyes
Examining Data:
Frequency Distribution: Identifies sets of scores (data)
and their frequencyRanks Data
TablesTables: Making a Frequency Distribution Table Begin with a sample (set) of scores
(data) Label the following Columns: X, tallies,
frequency (f), cumulative frequency (cf) Arrange the scores values under (X) in
descending order: highest to lowest. Tally the frequency each score occurs Record the (f) and cumulative frequency
(cf)
Like This:
73 // 2 2
72 /// 3 5
71 // 2 7
70 ///// 5 12
69 /// 3 15
68 / 1 16
X fTally cf
Pictures: Making a Pictures: Making a HistogramHistogram Turn the data table
“on its side” x axis = score value y axis = frequency of
occurrence A Histogram is just
another name for a Bar Graph
Create A Similar Graph: Use Height Data
Number ofOccurrences
2
4
6
8
10
12
KS SD IA NE CO MO AK
N = 38
State of Birth
Assignment:Create a Frequency Distribution
Table of Heights from the data generated in class last Friday (all 20 scores) – Make a Bar Graph
Read Lab 1: Introduction to Excel and Frequency Distributions
*Be sure you have “Installed/Refreshed MS Office”
What is this What is this Celestial Celestial Event?Event?
Describing Groups of Describing Groups of DataData
The Normal Distribution
(Will be Useful for Evaluation Comparisons!)
Types of Curves...
The Normal Curve:
Normal Curve: By Standard Deviation
34% of Scores in 1 SD
2 Standard deviations?
Curve “Skewness”
Making Sense of Tables and Pictures Tables and Histograms aren’t statistics -
they just “organize” sets of data Histograms give us a picture which is
often described as a “curve” Curves can be “Normal” with the hump
in the middle or, “Skewed” with the hump on either the
right or left of the total range of scores
Descriptive or Summary Statistics Moving from
pictures to formulas A set of
measurements is “measured” statistically
Two important properties measured by “Statistics:
Property # 1 Central
Tendency: Where is the “Middle” of the set of scores?
Is the Middle a good estimation of any given score?
Property # 2
Spread or Variability: How far away from the middle does the data “wander”
“Homogenous” samples have little spread
“Heterogeneous” samples have lots
Statistical Measures of Statistical Measures of Central TendencyCentral TendencyMean: The “average”Median: The middle of the
ordered scoresMode: The most frequently
occurring score(s)Which measure of Central tendency is best?
Statistical Measures of VariabilityStandard Deviation(s):
Average distance of the data from the mean
Variance (s2): Total spread of all the data
Assignment:
Problem Set #2: Calculating Mean, median, mode and standard deviation
Summary Sets of data can be organized into
Frequency Distribution Tables and Histograms
Curves can be described as Normal or Skewed
A set of data can be evaluated for Central Tendency (Mean, Median, Mode) and,
Spread or Variability (Standard Deviation and Variance)
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