This document provides an overview of statistics concepts for physical education. It discusses: - Types of data including qualitative, quantitative, discrete, and continuous variables. - Levels of measurement including nominal, ordinal, interval, and ratio scales. - Descriptive statistics for summarizing data such as measures of central tendency and variation. - Inferential statistics for making inferences about populations based on samples using techniques like hypothesis testing. - Key aspects of hypothesis testing including the null and alternative hypotheses, p-values, and types of errors.

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STATISTICS IN PHYSICAL EDUCATION
Dr. Parag Shah
H L College of Commerce
www.paragstatistics.wordpress.com
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SESSION 1
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Session Flow
• Data
• Types of Data
• Various measurements of data
• Data Analysis :
– Descriptive
– Inferential Statistics
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What is Data?
Data is a collection of facts or information from which
conclusions may be drawn
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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.

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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.

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Summary of Types of Variables

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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?
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Data Collection Methods
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• 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

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Levels of Measurements
• Categorical: Nominal, Ordinal
• Scale: Interval, Ratio
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Nominal-Level Data
Properties:
• Observations of a
qualitative variable can
only be classified and
counted.
• There is no particular
order to the labels.

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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.

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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.

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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.

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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.

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Summary of the Characteristics for Levels of
Measurement

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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

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Types of Analysis
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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.
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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

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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)

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1st
variable
Only 1 variable Scale Categorical
Scale Histogram Scatter plot Box-plot
Categorical Pie/ Bar Box-plot Stacked/ multiple
bar chart
Which graph?

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 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

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SESSION 2
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Session 2
• Inferential Statistics
• p value
• Null and Alternative Hypothesis
• Type I and Type II Error
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Inferential Statistics
The methods of inferential statistics are
• the estimation of parameter(s)
• testing of Statistical hypothesis
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Parameter and Statistics
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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

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Non – Parametric Tests
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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
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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

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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.
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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.
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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
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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.
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Alternative Hypothesis
The alternative hypothesis, denoted H1, is a
statement that is complementary to the Null
hypothesis.
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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
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Type1 and Type 2 Error
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• https://youtu.be/A3JQCsM2qfA
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Those who rule
DATA will rule the
entire world.
- Masayoshi Son
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