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**Descriptive Statistics**

Introduction to Study Skills & Research Methods (HL10040) Dr James Betts

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**Lecture Outline: Statistics Variables Levels of Measurement**

Measures of Central Tendency Distribution Variability.

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Statistics Descriptive Inferential Correlational

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Nominal Scale Ordinal Scale

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Interval Scale Ratio Scale

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**Quick Test Nominal, Ordinal, Interval or Ratio?**

Blood lactate concentration (mmol.l-1) Profile of Mood States (scale 1-7) Heart Rate (beats.min-1) Blood Group Bench Press 1RM (kg) Year of Birth (AD) Atmospheric Pressure (mmHg)

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**Système Internationale (SI) Units**

Seven ‘constant’* base units using the metric system Variable Unit Symbol Accepted Derivations Distance metre m ha for area; º for angle; #l or L for volume Mass* kilogram kg t Time second s min, h, d (not year) Temperature kelvin K Mole mole mol #l or L for volume Current ampere A Luminance candela cd Units always lower-case#, neither italicised nor pleuralised (i.e. kg not KGS) and with space between value and unit (inc. % but exc. º).

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**Discrete and Continuous Variables**

Discrete Variables: Continuous Variables:

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**Indicators of Central Tendency**

Mode Most Frequently Occurring Score Median Middle Score Mean Arithmetic Average.

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Normal Distribution

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Normal Distribution

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Normal Distribution

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**Non-Normal Distribution**

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**Hypothetical Investigation**

“The effect of 1 week placebo supplementation on press-up performance” 8 randomly sampled participants Performed as many press-ups as possible Supplemented with placebo tablets for 1 week

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Mean SD

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**Standard Error of the Mean (SEM)**

68.26% ????????????????????????????????????????????????????? Number of Press-ups

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**Standard Error of the Mean (SEM)**

SD n SEM =

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Mean SEM

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Median & Range or IQR The mean SD or SEM cannot be used for non-normally distributed data Instead the median is often plotted along with either the range or the IQR Raw Data: 8, 10, 15, 20, 55, 75, 120, 179

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**Put the data from each trial into SPSS…**

Week 2 Week 1

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**Select ‘Analyze’, ‘GLM’, ‘Repeated Measures’…**

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**Move variables from here…**

…to here, click ok

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ANOVA Output MSE n nCI = [criterion t (df)]

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**t – Distribution Table Degrees of Freedom Critical t-ratio 1 2 3 4 5 6**

(Google Search) Degrees of Freedom Critical t-ratio 1 2 3 4 5 6 7 8 12.71 4.30 3.18 2.78 2.57 2.45 2.37 2.31

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Mean nCI

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Selected Reading Hopkins W. G. (2000) A New View of Statistics [Online] Auckland: Internet Society for Sport Science. Available at: [accessed October 3rd 2005] Masson, M. E. J. and G. R. Loftus. Using confidence intervals for graphically based data interpretation. Canadian Journal of Experimental Psychology. 57: , 2003.

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