Lecture 7: Statistics in Kinesiology Research PDF

Statistical Concepts in Kinesiology Research Chapters 6 - 9 Dr. Andrew S. Perrotta University of Windsor...

Statistical Concepts in Kinesiology Research Chapters 6 - 9 Dr. Andrew S. Perrotta University of Windsor Faculty of Human Kinetics | Department of Kinesiology “The Numbers Will Love You Back in Return-I Promise” Martin Buchheit Buchheit M. (2016). The Numbers Will Love You Back in Return-I Promise. International journal of sports physiology and performance, 11(4), 551–554. ASP|2023 Learning Objectives I. Importance of Statistics in Kinesiology II. Statistical definitions III. Differences between groups IV. Relationship between variables V. APPLIED STATISTICS ….IT’S ABOUT DAMN TIME! ASP|2023 Importance of Statistics in Kinesiology Statistics is simply an objective means of interpreting a collection of observations. Statistical techniques are necessary for describing the characteristics of data (descriptive statistics) and for testing relationships or differences between sets of data (inferential statistics). *We use statistics to make inferences from data we have collected from a sample to the larger population from which that sample was taken.* ASP|2023 Importance of Statistics in Kinesiology To make comparisons or examine relationships between groups, we use statistical tools to determine whether observed differences or relationships are likely due to chance or a reliable (i.e. SIGNIFICANT) difference that would be expected in the larger population. Ribeiro, F., Longobardi, I., Perim, P., Duarte, B., Ferreira, P., Gualano, B., Roschel, H., & Saunders, B. (2021). Timing of Creatine Supplementation around Exercise: A Real Concern?. Nutrients, 13(8) ASP|2023 Importance of Statistics in Kinesiology Data analytics is the science of analyzing raw data to make conclusions about that information. * Data analytics help a business optimize its performance, perform more efficiently, maximize profit, or make more strategically-guided decisions.* https://www.investopedia.com/terms/d/data- analytics.asp ASP|2023 Importance of Statistics in Kinesiology Ward, Z. J., Bleich, S. N., Cradock, A. L., Barrett, J. L., Giles, C. M., Flax, C.,... & Gortmaker, S. L. (2019). Projected US state-level prevalence of adult obesity and severe obesity. New England Journal of Medicine, 381(25), 2440-2450. ASP|2023 Importance of Statistics in Kinesiology Is it possible?? Is it realistic?? Lean, M. E., et al., (2018). Primary care-led weight management for remission of type 2 diabetes (DiRECT): an open-label, cluster-randomised trial. Lancet, 391(10120), 541–551. ASP|2023 Importance of Statistics in Kinesiology https://www.schulich.uwo.ca/medicine/undergraduate/md_program/curriculum/index.html#YearOne ASP|2023 Importance of Statistics in Kinesiology Kochanek, K. D., Murphy, S. L., Xu, J., & Arias, E. (2019). National Vital Statistics Reports Volume 68, Number 9 June 24, 2019 Deaths: Final Data for 2017. Kyrou, I., Randeva, H. S., Tsigos, C., Kaltsas, G., & Weickert, M. O. (2018). Clinical problems caused by obesity. Endotext [Internet]. ASP|2023 Statistic al Definitio ns ASP|2023 Statistical Definitions Mean (µ) A statistical measure of central tendency that is the average score of a group of scores. Standard deviation (σ) An estimate of the variability of the scores of a group around the mean. Ex. Participant data is presented as a mean (± SD); 20.1 ± 1.2 yr. ASP|2023 Statistical Definitions Vertical Jump Height (cm) Vertical Jump Height (cm) Day#1 Testing Day#1 Testing ASP|2023 Statistical Definitions Confidence intervals (CI) display the probability that the true score will fall between a pair of lower and upper values around 10.0% the mean. d 8.0% d 6.0% c b b 90% CI = 90% confidence the 4.0% true value of the sample mean 2.0% falls within the error bar range. Δ PV% 0.0% -2.0% 95% CI = 95% confidence the -4.0% true value of the sample mean b -6.0% b b falls within the error bar range -8.0% d -10.0% 99% CI = 99% confidence the 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 true value of the sample mean Day falls within the error bar range Perrotta, A. S., White, M. D., Koehle, M. S., Taunton, J. E., & Warburton, D. E. (2018). Efficacy of Hot Yoga as a Heat Stress Technique for Enhancing Plasma Volume and Cardiovascular Performance in Elite Female Field Hockey Players. The Journal of Strength & Conditioning Research, 32(10), 2878-2887. ASP|2023 Statistical Definitions Central tendency A single score that best represents all the scores. Median A statistical measure of central tendency that is the middle score in a group. Mode A statistical measure of central tendency that is the most frequently occurring score of the group. ASP|2023  Normal Distribution is Statistical Definitions when the mean, median, and mode are at the same point (center of the distribution) and in which ±1SD from the mean includes 68% of the scores, ±2SD from the mean includes 95% of the scores, and ±3SD includes 99% of the scores. * We typically expect values of a sample (ex. VO2 Max) will be normally distributed * ASP|2023 Statistical Definitions Skewness A description of the direction of the hump of the curve of the data distribution and the nature of the tails of the curve. Woo, S. (2020). Modern definitions in reliability engineering. In Reliability Design of Mechanical Systems (pp. 53-99). Springer, Singapore. ASP|2023 Statistical Definitions Kurtosis A description of the vertical characteristic of the curve showing the data distribution, such as whether the curve is more peaked or flatter than the normal curve. ASP|2023 Statistical Definitions Parametric statistical test A test based on data assumptions of normal distribution, equal variance, and independence of observations. Nonparametric statistical test Any of a number of statistical techniques used when the data do not meet the assumptions required to perform parametric tests. ASP|2023 Statistical Issues in Research Planning and Evaluation Chapter 7 Hypothesis Testing Once you have identified the relevant literature and your research question, the next step is to construct a hypotheses that can be tested using data from your sample and the appropriate statistical test. Research hypothesis A hypothesis deduced from theory or induced from empirical studies that is based on logical reasoning and predicts the study’s outcome. Null hypothesis (HO) A hypothesis is used primarily in the statistical test for the reliability of the results that says that there are NO differences between treatments (or no relationships between variables). Alpha Alpha (𝛂) A level of probability (of chance occurrence) set by the experimenter before the study; sometimes referred to as level of significance. Probability (p) The odds that a certain event will occur. Important Points to Remember  Level of chance occurrence can vary from low to high.  It can never be eliminated.  For any given study, the probability of the findings being due to chance always exists.  The value of alpha is typically set at 0.05, and this tells us that 5 times out of 100 we are willing to mistakenly conclude that our findings are statistically significant when, in fact, they are actually chance findings. Alpha Increasing the alpha to 0.01 (ie. Your results are less than 1% chance due to error) DOES NOT INCREASE THE LEVEL OF SIGNIFICANCE IN YOUR RESULTS ! * It only DECREASES the chance your results are due to error * VERY IMPORTANT TO REMEMBER WHEN INTERPRETING RESULTS Ex. Using Alpha to Test Differences B/W Groups Held, N. J., Perrotta, A. S., Mueller, T., & Pfoh-MacDonald, S. J. (2022). Agreement of the Apple Watch® and Fitbit Charge® for recording step count and heart rate when exercising in water. Medical & Biological Engineering & Computing, 60(5), 1323-1331. ASP|2023 Ex. Using Alpha to Test Differences B/W Groups Research Hypothesis was… We expect significant differences in step count and heart rate between gold standard methods and each wearable device when exercising in water (ie. Apple & Fitbit). Null Hypothesis was…There will be no differences (p value < 0.05) when comparing heart rate and step count values in the Apple and Fitbit to the gold standard methods ASP|2023 Ex. Using Alpha to Test Differences B/W Groups Two-tailed t test A test that assumes that the difference between the two means could favor either direction. * Choose two-tail as we never TRULY know direction * One-tailed t test A test that assumes that the difference between the two means lies in one direction only. “VS ” ASP|2023 Ex. Using Alpha to Test Differences B/W Groups Is the difference b/w means significant (i.e. p < 0.05) and not be chance? Polar HR® Apple (Mean) Watch® (Mean) “VS ” ASP|2023 Ex. Using Alpha to Test Differences B/W Groups Paired t test (students t test) A type of t test used to determine whether two sample means differ reliably from each other. High Speed Photo Apple Watch ® Fitbit Charge ® t Test 1 Camera Gold Standard ‘vs’ Apple Step Count Step Count Step Count t Test 2 99 100 105 Gold Standard ‘vs’ 88 105 89 Fitbit 77 77 65 67 88 90 110 111 115 Ex. Using Alpha to Test Differences B/W Groups Analysis of variance (ANOVA) A test that allows the evaluation of the null hypothesis between two or more group groups. ‘vs ‘vs Gold ’ ’ Standard ASP|2023 Ex. Using Alpha to Test Differences B/W Groups Held, N. J., Perrotta, A. S., Mueller, T., & Pfoh-MacDonald, S. J. (2022). Agreement of the Apple Watch® and Fitbit Charge® for recording step count and heart rate when exercising in water. Medical & Biological Engineering & Computing, 60(5), 1323-1331. ASP|2023 Meaningfulness (Effect Size) Effect size (Standardized Mean Differences) The standardized value that is the difference between the means divided by the standard deviation. Meaningfulness The importance or practical significance of an effect or relationship. Effect size gives us an indication of the magnitude of the effect/difference between means. M1 = Gold Standard M2 = Apple Watch ® S = Pooled Standard Deviation from both samples (ie. Devices) Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). New Jersey: Lawrence Erlbaum ASP|2023 Meaningfulness (Effect Size) Visual Comparison of ES ES represents the amount of STANDARD Apple Watch ® DEVIATIONS each Gold Standard group is separate by. Magnitude of Difference Adapted from Hopkins., 2004 Hopkins, W. G. (2004). How to interpret changes in an athletic performance test. Sportscience, 8, 1-7. ASP|2023 Meaningfulness (Effect Size) Magnitude ES Size Interpretation * Allows you to Insignificant / Trivial < 0.20 quantify the difference Small 0.20 – 0.59 between means/groups* Moderate 0.60 – 1.19 Large 1.20 – 1.99 Very Large 2.00 – 3.99 Extremely Large > 4.00 Adapted from Hopkins et al., 2009 Hopkins, W., Marshall, S., Batterham, A., & Hanin, J. (2009). Progressive statistics for studies in sports medicine and exercise science. Medicine and Science in Sports and Exercise, 41(1), 3. ASP|2023 Relationship Between Groups Correlation A statistical technique used to determine the relationship between two or more variables. Dependent Variable Independent Variable Held, N. J., Perrotta, A. S., Mueller, T., & Pfoh-MacDonald, S. J. (2022). Agreement of the Apple Watch® and Fitbit Charge® for recording step count and heart rate when exercising in water. Medical & Biological Engineering & Computing, 60(5), 1323-1331. ASP|2023 Relationship Between Groups Coefficient of correlation (r) A quantitative value of the linear relationship between two or more variables. It can range from 0.00 to 1.0 in either a positive or negative direction. Positive Correlation A linear relationship between two variables in which a small value for one variable is associated with a small value for another variable, and a large value for one variable is associated with a large value for the other. r = POSITIVE VALUE (r > 0.00) Held, N. J., Perrotta, A. S., Mueller, T., & Pfoh-MacDonald, S. J. (2022). Agreement of the Apple Watch® and Fitbit Charge® for recording step count and heart rate when exercising in water. Medical & Biological Engineering & Computing, 60(5), 1323-1331. ASP|2023 Relationship Between Groups Coefficient of correlation (r) A quantitative value of the linear relationship between two or more variables. It can range from 0.00 to 1.0 in either a positive or negative direction. Negative Correlation A linear relationship between two variables in which a small value for the first variable is associated with a large value for the second variable, and a large value for the first variable is associated with a small value for the second variable. r = NEGATIVE value (r < 0.00) ASP|2023 Relationship Between Groups nearly trivia sma modera larg very perfec perfec l ll te e large t t Correlatio 0.00 0.10 0.30 0.50 0.70 0.90 1.0 n (r) Adapted from Hopkins., 2004 Hopkins, W. G. (2004). How to interpret changes in an athletic performance test. Sportscience, 8, 1-7. ASP|2023 Using Regression for Prediction R2 (Coefficient of Determination) A method of interpreting the proportion of variation between the dependent variable (ex. Apple Watch®) to the independent variable (ex. Polar® HR Monitor) that can be EXPLAINED and used to PREDICT an outcome/score. y equation (ie. Apple Watch® HR SE = 0.01 Value) allows you to predict the true value (ie. Polar® HR value) Standard Error (SE) = The correction (ie. error value) you must ± to the y value/score for an accurate HR prediction ASP|2023 Applied Research Applied Research “Surely God loves a p value of 0.06 nearly as much as the 0.05” The choice of a p < 0.05 is essentially arbitrary and, hence, a finding of p = 0.06 is not very different from p < 0.05. It is important to consider the magnitude of the observable effects relative to both the objective they are trying to achieve and any risks or costs of the treatment. (Rosnow & Rosenthal, 1989, p. 1277) ASP|2023 Applied Statistics for Kinesiology Viewed as CONTROVERSIAL……I DON’T CARE! Thomas Bayes, Born 1701 Died 1761  Was an English statistician, philosopher and Presbyterian minister.  Known for formulating a specific case of the theorem that bears his name: Bayes' theorem.  Bayes never published what would become his most famous accomplishment; his notes were edited and published posthumously by Richard Price. ASP|2023 Applied Statistics for Kinesiology Bayesian statistics is where available knowledge (i.e. previous research) is used in your statistical analysis to help decide clinical significance. LET’S DO THIS! ASP|2023 Applied Statistics for Kinesiology Bayesian Statistics I. You are the expert. (i.e. You define clinical significance) II. You take on all the risk/stress and responsibility when using Bayesian statistics Athletic Assessment Reliability of Test (i.e. Difference b/w Tests) 1-RM Leg Press (kg) 10 -14 % Currell, K., & Jeukendrup, A. E. (2008). Validity, reliability and sensitivity of measures of sporting performance. Sports Medicine, 38(4), 297-316. VO2 Max (mL·kg-1·min-1) ≤ 6.0% Hopkins, W. G., Schabort, E. J., & Hawley, J. A. (2001). Reliability of power in physical performance tests. Sports Medicine, 31(3), 211-234. R.O.M (degreeso of knee 43% Akizuki, K., Yamaguchi, K., Morita, Y., & Ohashi, Y. (2016). The effect of proficiency level on measurement error of range of motion. Journal of physical therapy science, 28(9), 2644–2651. joint) ASP|2023 Applied Statistics for Kinesiology I. People are afraid to make mistakes… II. People do not understand clinical significance…(Ex. non practitioners) III. It is easier to rely on a BLACK ‘or’ WHITE answer (i.e. p value) ASP|2023 Applied Statistics for Kinesiology a priori a statement, that is based on previous research/findings, that is used to define the magnitude of change (SWC) deemed as “significant”.  Forces researchers to adopt a conscious process when analyzing their data.  The importance of an appropriate SWC definition is often overlooked. Buchheit, M. (2016). The numbers will love you back in return—I promise. International journal of sports physiology and performance, 11(4), 551-554. ASP|2023 Applied Statistics for Kinesiology Clinically Statistically Harmful Trivial Beneficial Significant? significant? Beneficial Yes Beneficial Yes Trivial Is the magnitude Beneficial No of change that is Trivial No considered as the Trivial Yes Bayes reasoning for “Smallest Worthwhile Trivial No using his approach Change” Trivial No to statistics Harmful Yes Harmful Yes Unclear No negative 0 positive value of effect statistic Adapted from Hopkins., 2004 Hopkins, W. G. (2004). How to interpret changes in an athletic performance test. Sportscience, 8, 1-7. ASP|2023 Importance of Applied Statistics for Kinesiology 1. p values are sample-size dependent (the greater the n, the lower the p value) irrespective of the effect size. Ex. While it can be concluded that the nutritional supplement is ineffective with a sample of n = 12 athletes (p > 0.05), the same comparison may turn useful with n = 14 (p < 0.05). *The drop-out of a few athletes, or the lucky involvement of 2 more subjects can induce Buchheit, M. (2016). The numbers will love you back in return—I promise. International journal of sports physiology and performance, 11(4), 551-554. a 180 degree change in a study conclusion* ASP|2023 Importance of Applied Statistics for Kinesiology 2. Significance does NOT inform on the magnitude of change, yet the magnitude of change is what matters the most.  An effect size of 0.50 (moderate) may be accompanied with a p = 0.06… An effect size of 0.10 (trivial) may accompanied with a p = 0.01… Buchheit, M. (2016). The numbers will love you back in return—I promise. International journal of sports physiology and performance, 11(4), 551-554. ASP|2023 Importance of Applied Statistics for Kinesiology 3. The examination of the magnitudes helps provide better research questions. Typical hypotheses that do not have clear foundations Ex. “We hypothesized that the new supplement would be beneficial for performance”) ….can be replaced by a simpler and more relevant… Ex. “Our aim was to quantify the performance benefit of that supplement, if any”. ASP|2023