Chapter 8Chapter 8

Practical Inferential Statistics Practical Inferential Statistics for the Physical Activity for the Physical Activity and Health Professionsand Health Professions

Inferential StatisticsInferential Statistics

Field of study devoted to using statistical Field of study devoted to using statistical probability tools:probability tools:

• To help people think about data.To help people think about data.• To make conclusions about populations on the To make conclusions about populations on the

basis of data from samples.basis of data from samples.• To help someone become a better teacher, To help someone become a better teacher,

coach, therapist, or fitness professional—by coach, therapist, or fitness professional—by being able to evaluate reports and understand being able to evaluate reports and understand research (and where they may go wrong).research (and where they may go wrong).

CorrelationCorrelation

• Measures the degree of relationship Measures the degree of relationship (strength and direction) between two (strength and direction) between two variables.variables.

• Does not explain Does not explain why why variables move variables move as they do; only that they do.as they do; only that they do.

Correlation CoefficientCorrelation Coefficient

• Ranges between 0 and +1 and Ranges between 0 and +1 and –1–1• 0 indicates no relationship0 indicates no relationship• +1 indicates a strong relationship+1 indicates a strong relationship• ––1 indicates a negative relationship1 indicates a negative relationship

• Positive/negative sign indicates the Positive/negative sign indicates the directiondirection (not the strength) of the (not the strength) of the relationship.relationship.

Regression EquationRegression Equation

• Defined: The process of using the Defined: The process of using the correlation between two variables to correlation between two variables to develop an equation for the line of best develop an equation for the line of best fit, or trendline.fit, or trendline.

y value = the slope y value = the slope ** the the xx value + value + y y intercept intercept (the point on (the point on yy where where xx = 0) = 0)

y = mx + by = mx + b

• Can be used for making predictions.Can be used for making predictions.

Sample Regression Equation Sample Regression Equation and Line of Best Fit and Line of Best Fit

(Relationship Between Pull-Ups and Fatness)(Relationship Between Pull-Ups and Fatness)

Negative (Indirect) CorrelationsNegative (Indirect) Correlations

• When an increase in one variable goes When an increase in one variable goes along with a decrease in another variable along with a decrease in another variable there is a negative relationship.there is a negative relationship.– For example, an increase in physical activity For example, an increase in physical activity

and a decrease in weight.and a decrease in weight.

• Does Does notnot indicate the strength of the indicate the strength of the relationship.relationship.

A Weak CorrelationA Weak Correlation

A Strong CorrelationA Strong Correlation

Multiple CorrelationMultiple Correlation

• A measurement that uses several A measurement that uses several independent measures to predict the independent measures to predict the success of an outcome.success of an outcome.– For example, look at variables of size, speed, For example, look at variables of size, speed,

strength, years of experience, age, etc., strength, years of experience, age, etc., when predicting an athlete’s playing success.when predicting an athlete’s playing success.

• Modeling: Determining which variables Modeling: Determining which variables contribute the most to a prediction.contribute the most to a prediction.

Complex Comparisons Complex Comparisons

• Comparisons of sample means:Comparisons of sample means:– To make inferences about a populationTo make inferences about a population– To compare different measurement To compare different measurement

methods and statisticsmethods and statistics

• Tests for comparisons:Tests for comparisons:– t-tests (two group means)t-tests (two group means)– Analysis of variance (ANOVA; three or Analysis of variance (ANOVA; three or

more group means)more group means)

ProbabilitiesProbabilities

• Means and probabilities: Means and probabilities: – The p value is the probability that two means The p value is the probability that two means

are different only by chance.are different only by chance.

• Correlations and probabilities: Correlations and probabilities: – The p value is the probability that random The p value is the probability that random

sampling would result in a correlation sampling would result in a correlation coefficient as different from zero as the one coefficient as different from zero as the one that was found.that was found.

Errors in ProbabilitiesErrors in Probabilities

• Type I error: Type I error: – The risk of assuming a difference The risk of assuming a difference

exists when none really does. exists when none really does.

• Type II error: Type II error: – A failure to find a difference between A failure to find a difference between

means that really does exist. means that really does exist.

Implications of ErrorsImplications of Errors

• When doing your own research: When doing your own research: – Think about the implications of errors before Think about the implications of errors before

doing calculations.doing calculations.

• When reading someone else’s research:When reading someone else’s research:– Evaluate the possibility that errors were Evaluate the possibility that errors were

made; if it appears that possible errors exist, made; if it appears that possible errors exist, confidence in the study’s conclusions may be confidence in the study’s conclusions may be lowered.lowered.

Statistical PowerStatistical Power

• The ability to find the difference between The ability to find the difference between means.means.

• Dependent on four factors:Dependent on four factors:– Size of the sampleSize of the sample– Size of the effectSize of the effect– p valuep value– Standard deviation; variability of the groupsStandard deviation; variability of the groups

Misusing StatisticsMisusing Statistics

• Use of non-normal samplesUse of non-normal samples

• Problems with sample sizes (either Problems with sample sizes (either too large or too small)too large or too small)

• Over-reliance on group means (at Over-reliance on group means (at the expense of the individual the expense of the individual person)person)

• Substitution of statistics for common Substitution of statistics for common sensesense

Your ViewpointYour Viewpoint

• Can you think of an example Can you think of an example (perhaps from the world of sports) (perhaps from the world of sports) of a time when statistics were of a time when statistics were misused? misused?

• How? What were the results?How? What were the results?

Example of Non-Normal DataExample of Non-Normal Data