Statistics for Physical Education
- 1. 1-1 STATISTICS IN PHYSICAL EDUCATION Dr. Parag Shah H L College of Commerce www.paragstatistics.wordpress.com 1
- 3. 1-3 Session Flow • Data • Types of Data • Various measurements of data • Data Analysis : – Descriptive – Inferential Statistics 3
- 4. 1-4 What is Data? Data is a collection of facts or information from which conclusions may be drawn 4
- 5. 1-5 Types of Data A. Qualitative or Attribute data - the characteristic being studied is nonnumeric. E.g.: Gender, religious affiliation, state of birth, country representing, words, images, videos B. Quantitative data - information is reported numerically. E.g.: time (in seconds) for 400 mts race, Prize money won by a tennis player , or number of boundaries scored in a match.
- 6. 1-6 Quantitative Variables - Classifications Quantitative variables can be classified as either discrete or continuous. A. Discrete variables: can only assume certain values EXAMPLE: the number of goals in a football match, or the number of wickets by a bowler in a cricket match (1,2,3,…,etc.) B. Continuous variable can assume any value within a specified range. EXAMPLE: the height of an athlete or the weight of a boxer.
- 7. 1-7 Summary of Types of Variables
- 8. 1-8 Data Collection The 5 W’s of data collection are: 1.What data is to be collected? 2.From whom data is to be collected? 3.Who will collect data? 4.From where the data will be collected? 5.When is the data collected? 8
- 9. 1-9 Data Collection Methods 9 • Involves data collection directly from the subjects by the researcher or trained data collector. • e.g. Surveys, Interview, Observations etc.Primary Data collection method • It involves of use of the data that were collected for various purposes other than current research. • e.g. diaries, nurses notes, care plans, patient medication record, statistical abstracts, census reports neither published or unpublished data Secondary Data collection method
- 10. 1-10 Levels of Measurements • Categorical: Nominal, Ordinal • Scale: Interval, Ratio 10
- 11. 1-11 Nominal-Level Data Properties: • Observations of a qualitative variable can only be classified and counted. • There is no particular order to the labels.
- 12. 1-12 Ordinal-Level Data Properties: • Data classifications are represented by sets of labels or names (high, medium, low) that have relative values. • Because of the relative values, the data classified can be ranked or ordered.
- 13. 1-13 Interval-Level Data Properties: • Data classifications are ordered according to the amount of the characteristic they possess. • Equal differences in the characteristic are represented by equal differences in the measurements. Example: Women’s dress sizes listed on the table.
- 14. 1-14 Ratio-Level Data Practically all quantitative data is recorded on the ratio level of measurement. Ratio level is the “highest” level of measurement. Properties: • Data classifications are ordered according to the amount of the characteristics they possess. • Equal differences in the characteristic are represented by equal differences in the numbers assigned to the classifications. • The zero point is the absence of the characteristic and the ratio between two numbers is meaningful.
- 15. 1-15 Four Levels of Measurement Nominal level - data that is classified into categories and cannot be arranged in any particular order. EXAMPLES: eye color, gender, religious affiliation. Ordinal level – data arranged in some order, but the differences between data values cannot be determined or are meaningless. EXAMPLE: During a taste test of 4 soft drinks, Thumps Up was ranked number 1, Sprite number 2, Seven-up number 3, and Fanta number 4. Interval level - similar to the ordinal level, with the additional property that meaningful amounts of differences between data values can be determined. There is no natural zero point. EXAMPLE: Temperature on the Fahrenheit scale., size of garment, Likert’s scale Ratio level - the interval level with an inherent zero starting point. Differences and ratios are meaningful for this level of measurement. EXAMPLES: Monthly income of surgeons, or distance traveled by manufacturer’s representatives per month.
- 16. 1-16 Summary of the Characteristics for Levels of Measurement
- 17. 1-17 Why to Know the Level of Measurement of a Data? • The level of measurement of the data dictates the calculations that can be done to summarize and present the data. • To determine the statistical tests that should be performed on the data
- 19. 1-19 Types of Analysis • Descriptive statistics uses the data to provide descriptions of the population, either through numerical calculations or graphs or tables. • Inferential statistics makes inferences and predictions about a population based on a sample of data taken from the population in question. 19
- 20. 1-20 Descriptive Statistics Summarizing Data: – Central Tendency (or Groups’ “Middle Values”) • Mean • Median • Mode – Variation (or Summary of Differences Within Groups) • Range • Interquartile Range • Variance • Standard Deviation
- 21. 1-21 Choosing summary statistics Which average and measure of spread? Scale Normally distributed Mean (Standard deviation) Skewed data Median (Interquartile range) Categorical Ordinal: Median (Interquartile range) Nominal: Mode (None)
- 22. 1-22 1st variable Only 1 variable Scale Categorical Scale Histogram Scatter plot Box-plot Categorical Pie/ Bar Box-plot Stacked/ multiple bar chart Which graph?
- 23. 1-23 Bar chart Clustered bar charts (two categorical variables) Histogram (can be plotted against a categorical variable) Box & Whisker plot (can be plotted against a categorical variable) Dot plot (can be plotted against a categorical variable) Scatter plot (two continuous variables) Mean Median Standard deviation Range (Min, Max) Inter-quartile range (LQ, UQ) Flow chart of commonly used descriptive statistics and graphical illustrations Frequency Percentage (Row, Column or Total) Exploring data Descriptive statistics Graphical illustrations Categorical data Continuous data: Measure of location Continuous data: Measure of variation Categorical data Continuous data
- 25. 1-25 Session 2 • Inferential Statistics • p value • Null and Alternative Hypothesis • Type I and Type II Error 25
- 26. 1-26 Inferential Statistics The methods of inferential statistics are • the estimation of parameter(s) • testing of Statistical hypothesis 26
- 28. 1-28 Parametric or Non-parametric? •Parametric tests are restricted to data that: 1) show a normal distribution 2) are independent of one another 3) are on the same continuous scale of measurement •Non-parametric tests are used on data that: 1) show an other-than normal distribution 2) are dependent or conditional on one another 3) in general, do not have a continuous scale of measurement
- 29. 1-29 29
- 30. 1-30 Non – Parametric Tests 30
- 31. 1-31 Parametric & Non-Parametric tests Purpose of test Parametric Test Non-Parametric Test Compare central value( Mean / Median) with specific value One sample t / Z test Wilcoxon Signed Rank Compare central values of two independent samples Two sample t / Z test Mann -Whitney Compare central values of two dependent samples Paired t test Wilcoxon Signed Rank Compare central values of three or more samples ( One Variable) One Way ANOVA Kruskal - Wallis Compare central values of three or more samples ( Two Variable) Two Way ANOVA Friedman Compare independence of two categorical variables Chi – Square 31
- 32. 1-32 32 p-value p-value is the probability the test statistic would take a value as extreme or more extreme than observed test statistic, when H0 is true
- 33. 1-33 p value • Smaller-and-smaller p-values → stronger-and- stronger evidence against H0 • For typical analysis, using the standard α = 0.05 cutoff, the null hypothesis is - rejected when p <= .05 and - not rejected when p > .05. 33
- 34. 1-34 Hypothesis • A hypothesis is a statement regarding a characteristic of one or more populations. • Hypothesis testing is a procedure, based on sample evidence and probability, used to test statements regarding a characteristic of one or more populations. 34
- 35. 1-35 Steps of Hypothesis Testing • Define Null Hypothesis • Decide Alternative Hypothesis • Calculate test statistics • Find the table of test statistics based on level of significance • Give the conclusion based on test statistics and it’s table value 35
- 36. 1-36 Null Hypothesis The null hypothesis, denoted H0, is a statement to be tested. The null hypothesis is a statement of no change, no effect or no difference and is assumed true until evidence indicates otherwise. 36
- 37. 1-37 Alternative Hypothesis The alternative hypothesis, denoted H1, is a statement that is complementary to the Null hypothesis. 37
- 38. 1-38 Different Alternative Hypothesis 1.Equal versus not equal hypothesis (two-tailed test) H0: parameter = some value H1: parameter ≠ some value 2. Equal versus less than (One- tailed, left-tailed test) H0: parameter = some value H1: parameter < some value 3. Equal versus greater than (One- tailed, right-tailed test) H0: parameter = some value H1: parameter > some value 38
- 39. 1-39 Type1 and Type 2 Error 39
- 41. 1-41 Those who rule DATA will rule the entire world. - Masayoshi Son 41