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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). Correlation • Measures the degree of relationship (strength and direction) between two variables. • 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 relationship. 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 relationship. 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) Probabilities • 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 lowered. Statistical Power • The ability to find the difference between means. • 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 person) • Substitution of statistics for common sense Your Viewpoint • Can you think of an example (perhaps from the world of sports) of a time when statistics were misused? • How? What were the results? Example of Non-Normal Data