PED 471: Height Histogram Spring 2001

Introduction to Statistics Giving Meaning to Measurement Chapter 4:94-104

If You Don’t Agree With 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 Measurements ACCURATE DATA: Depends on good tests and qualified “testers” GOOD LOGIC: Depends on appropriate evaluations of the assessments.

Test Validity Comes Later… First let’s take a look at “Evaluation” How can statistics help us evaluate data?

Evaluate these scores Before SupplementAfter Sub Sub Sub Sub Sub Sub Sub Sub Sub Sub Sub Sub

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 “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: Constants: Qualities that never change in a selected population E.g. female students at WSC – Female is constant Variables: Qualities expected to change or vary within a population or between individuals: E.g. The GPA of female students at WSC

Types of Scores Nominal: 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 of 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 VO 2 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 students Complete “Stat Problems #1” (Math for Muscle Heads)

DATA EVALUATION: “Draw Me a Picture”

Organizing the Data Tables: Ordering the data Pictures: (Histograms) Seeing a pattern in the data Formulas: Trusting your eyes

Examining Data: Frequency Distribution: Identifies sets of scores (data) and their frequency Ranks Data

Tables Tables: 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//22 72///35 71//27 70/////512 69///315 68/116 XfTallycf

Pictures: Making a Histogram 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 of Occurrences KSSDIANE COMO 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 CelestialEvent?

Describing Groups of Data The Normal Distribution (Will be Useful for Evaluation Comparisons!)

Types of Curves... The Normal Curve 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 Central Tendency Mean: The “average” Median: The middle of the ordered scores Mode: The most frequently occurring score(s) Which measure of Central tendency is best?

Statistical Measures of Variability Standard Deviation(s): Average distance of the data from the mean Variance (s 2 ): 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)