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)