Chapter 1Chapter 1

Measurement, Statistics, and Measurement, Statistics, and ResearchResearch

What is Measurement?What is Measurement?

Measurement is the process of Measurement is the process of comparing a value to a standardcomparing a value to a standard

Statistics is a mathematical tool Statistics is a mathematical tool used for interpretationused for interpretation

Precision is essential: if the Precision is essential: if the measurement is not PRECISE, the measurement is not PRECISE, the results cannot be TRUSTEDresults cannot be TRUSTED

What is Measurement?What is Measurement?

To be acceptable the data must beTo be acceptable the data must be– Valid, Reliable & objectiveValid, Reliable & objective

Valid (must be compared to known Valid (must be compared to known value or method)value or method)

Reliable – is the measurement Reliable – is the measurement consistent?consistent?

Objective – free from BIAS?Objective – free from BIAS?

Steps in Measurement Steps in Measurement ProcessProcess1.1. Object to be measured is identified Object to be measured is identified

and definedand defined2.2. The standard to which the object is to The standard to which the object is to

be compared is identified and be compared is identified and defineddefined

3.3. A comparison of the object to the A comparison of the object to the standard is madestandard is made

4.4. A quantitative statement of the A quantitative statement of the relationship between the standard an relationship between the standard an object is made (statistical evaluation)object is made (statistical evaluation)

Variables and Variables and ConstantsConstants A variable is a characteristic that A variable is a characteristic that

can assume more than one valuecan assume more than one value A constant can assume only one A constant can assume only one

valuevalue

Types of VariablesTypes of Variables

Continuous variable – can assume Continuous variable – can assume any value (ht, wt)any value (ht, wt)

Discrete variable – limited to Discrete variable – limited to certain values: integers or whole certain values: integers or whole numbers (2.5 children?)numbers (2.5 children?)

Classification of Data Classification of Data or Level of Measurementor Level of Measurement

Nominal Scale: mutually exclusive (male, Nominal Scale: mutually exclusive (male, female)female)

Ordinal Scale: gives quantitative order to the Ordinal Scale: gives quantitative order to the variable, but it DOES NOT indicate how much variable, but it DOES NOT indicate how much better one score is than another (RPE of 2 is better one score is than another (RPE of 2 is not twice of 1)not twice of 1)

Interval Scale: has equal units and zero is not Interval Scale: has equal units and zero is not an absence of the variable (temperature)an absence of the variable (temperature)

Ratio Scale: based on order, has equal Ratio Scale: based on order, has equal distance between scale points, and zero is an distance between scale points, and zero is an absence of valueabsence of value

Research Design & Statistical Research Design & Statistical AnalysisAnalysis

Research is a technique for solving Research is a technique for solving problems. Identifying the problem is problems. Identifying the problem is criticalcritical

Types of Research:Types of Research:– HistoricalHistorical– DescriptiveDescriptive– Experimental: involves manipulating and Experimental: involves manipulating and

controlling variables to solve a problemcontrolling variables to solve a problem Hypothesis: Hypothesis:

– an educated guessan educated guess– based on prior researchbased on prior research– Can be testedCan be tested

Hypothesis TestingHypothesis Testing

Research Hypothesis (HResearch Hypothesis (H11): predicts ): predicts relationships or differences between relationships or differences between groupsgroups

Null Hypothesis (HNull Hypothesis (H00): predicts NO ): predicts NO relationship or differences between groupsrelationship or differences between groups

The statistical analysis reports the The statistical analysis reports the PROBABILITY that the results would if HPROBABILITY that the results would if H00 were truewere true

If the probability (1 in 100) or (5 in 100) If the probability (1 in 100) or (5 in 100) that the null is true, we REJECT the null that the null is true, we REJECT the null and ACCEPT Hand ACCEPT H11

NOTE: NOTE: We never PROVED EITHER!We never PROVED EITHER!

Independent & Dependent Independent & Dependent VariablesVariables

Independent Variable: totally free to Independent Variable: totally free to vary. (balance is independent of VOvary. (balance is independent of VO22))

Dependent Variable: NOT free to vary Dependent Variable: NOT free to vary (ht and wt)(ht and wt)

The INDEPENDENT VARIABLE is The INDEPENDENT VARIABLE is controlled by the researcher (effects of controlled by the researcher (effects of exercise on body fat) on body fat)

The DEPENDENT VARIABLE is the The DEPENDENT VARIABLE is the variable being studied (effects of variable being studied (effects of exercise on exercise on body fatbody fat))

Internal ValidityInternal Validity

Internal Validity: Internal Validity: – refers to the design of the studyrefers to the design of the study– All potential intervening variables must All potential intervening variables must

be controlled (rat studies are easier to be controlled (rat studies are easier to control)control)

– Failure to use a control group harms Failure to use a control group harms internal validityinternal validity

– Instrument Error reduces internal validityInstrument Error reduces internal validity– Investigator Bias reduces internal Investigator Bias reduces internal

validityvalidity

External ValidityExternal Validity

External Validity refers to the ability to External Validity refers to the ability to generalize the results of a SAMPLE to generalize the results of a SAMPLE to the POPULATION (rat studies don’t the POPULATION (rat studies don’t always generalize to humans)always generalize to humans)

If a sample is not RANDOM it may not If a sample is not RANDOM it may not represent the populationrepresent the population

The process of generalizing from a The process of generalizing from a SAMPLE to a POPULATION is SAMPLE to a POPULATION is statistical statistical inferenceinference

Statistical InferenceStatistical Inference

A Population is a group with a common A Population is a group with a common characteristiccharacteristic

A population is usually large and it is difficult A population is usually large and it is difficult to measure all membersto measure all members

To make inference about a population we take To make inference about a population we take a representative sample (RANDOM)a representative sample (RANDOM)

In a random sample each member of the In a random sample each member of the population is equally likely to be selectedpopulation is equally likely to be selected

A stratified sample is a sample that is selected A stratified sample is a sample that is selected according to existing subcategories (rep, dem, according to existing subcategories (rep, dem, ind)ind)

A sample cannot accurately represent the A sample cannot accurately represent the population unless it is drawn without BIASpopulation unless it is drawn without BIAS

In a bias free sample selection of one member In a bias free sample selection of one member does not affect to selection of future subjectsdoes not affect to selection of future subjects

Parameters and Parameters and StatisticsStatistics A A parameterparameter represents the represents the

populationpopulation A A statisticstatistic represents the represents the samplesample The difference between a statistic The difference between a statistic

and a parameter is the result of and a parameter is the result of sampling errorsampling error

Probability and Hypothesis Probability and Hypothesis TestingTesting

Statistics is the science of making Statistics is the science of making educated guesseseducated guesses

Statistics allow us to make a Statistics allow us to make a statement and then cite the odds statement and then cite the odds that it is correctthat it is correct

A random sample of 200 females A random sample of 200 females have a mean ht of 5’ 2” ± 2”. The have a mean ht of 5’ 2” ± 2”. The odds are 95 to 5 that this mean is odds are 95 to 5 that this mean is correct.correct.

Probability and Hypothesis Probability and Hypothesis TestingTesting

A random sample of 200 females have A random sample of 200 females have a mean ht of 5’ 2” ± 2”. a mean ht of 5’ 2” ± 2”.

This means that the odds are 95 to 5 This means that the odds are 95 to 5 that the true mean is between 5’ and that the true mean is between 5’ and 5’ 4”5’ 4”

If a sample results in a mean of 5’ 3” If a sample results in a mean of 5’ 3” we accept a hypothesis that the ht is we accept a hypothesis that the ht is 5’ 3” because it lies within the limits 5’ 3” because it lies within the limits (5’ and 5’ 4”)(5’ and 5’ 4”)

Theories and HypothesesTheories and Hypotheses

A theory is a belief regarding a A theory is a belief regarding a concept or a series of related concept or a series of related conceptsconcepts

Many hypotheses can be TESTEDMany hypotheses can be TESTED If a sufficient number of results If a sufficient number of results

confirm the theory it is accepted confirm the theory it is accepted as trueas true

Mental practice improves Mental practice improves performanceperformance

Misuse of StatisticsMisuse of Statistics

Abdominal Exercise devices?Abdominal Exercise devices? Toothpaste?Toothpaste? Examples of statistics that may or may Examples of statistics that may or may

not be truenot be true Lack of random sample, small sample Lack of random sample, small sample

size, research is PAIDsize, research is PAID Outliers: extreme scores (more than 3 Outliers: extreme scores (more than 3

SD)SD) Mean income (Income is a skewed Mean income (Income is a skewed

distribution)distribution)