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Chapter 8
Practical Inferential Statistics
for the Physical Activity
and Health Professions
Inferential Statistics
Field of study devoted to using statistical
probability tools:
• To help people think about data.
• To make conclusions about populations on the
basis of data from samples.
• To help someone become a better teacher,
coach, therapist, or fitness professional—by
being able to evaluate reports and understand
research (and where they may go wrong).
• Measures the degree of relationship
(strength and direction) between two
• Does not explain why variables move
as they do; only that they do.
Correlation Coefficient
• Ranges between 0 and +1 and –1
• 0 indicates no relationship
• +1 indicates a strong relationship
• –1 indicates a negative relationship
• Positive/negative sign indicates the
direction (not the strength) of the
Regression Equation
• Defined: The process of using the
correlation between two variables to
develop an equation for the line of best
fit, or trendline.
y value = the slope * the x value + y intercept
(the point on y where x = 0)
y = mx + b
• Can be used for making predictions.
Sample Regression Equation
and Line of Best Fit
(Relationship Between Pull-Ups and Fatness)
Negative (Indirect) Correlations
• When an increase in one variable goes
along with a decrease in another variable
there is a negative relationship.
– For example, an increase in physical activity
and a decrease in weight.
• Does not indicate the strength of the
A Weak Correlation
A Strong Correlation
Multiple Correlation
• A measurement that uses several
independent measures to predict the
success of an outcome.
– For example, look at variables of size, speed,
strength, years of experience, age, etc.,
when predicting an athlete’s playing success.
• Modeling: Determining which variables
contribute the most to a prediction.
Complex Comparisons
• Comparisons of sample means:
– To make inferences about a population
– To compare different measurement
methods and statistics
• Tests for comparisons:
– t-tests (two group means)
– Analysis of variance (ANOVA; three or
more group means)
• Means and probabilities:
– The p value is the probability that two means
are different only by chance.
• Correlations and probabilities:
– The p value is the probability that random
sampling would result in a correlation
coefficient as different from zero as the one
that was found.
Errors in Probabilities
• Type I error:
– The risk of assuming a difference
exists when none really does.
• Type II error:
– A failure to find a difference between
means that really does exist.
Implications of Errors
• When doing your own research:
– Think about the implications of errors before
doing calculations.
• When reading someone else’s research:
– Evaluate the possibility that errors were
made; if it appears that possible errors exist,
confidence in the study’s conclusions may be
Statistical Power
• The ability to find the difference between
• Dependent on four factors:
– Size of the sample
– Size of the effect
– p value
– Standard deviation; variability of the groups
Misusing Statistics
• Use of non-normal samples
• Problems with sample sizes (either
too large or too small)
• Over-reliance on group means (at
the expense of the individual
• Substitution of statistics for common
Your Viewpoint
• Can you think of an example
(perhaps from the world of sports)
of a time when statistics were
• How? What were the results?
Example of Non-Normal Data