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

Lecture Outline: Statistics Variables Levels of Measurement Measures of Central Tendency Distribution Variability.

Statistics Descriptive Inferential Correlational

Nominal Scale Ordinal Scale

Interval Scale Ratio Scale

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)

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).

Discrete and Continuous Variables Discrete Variables: Continuous Variables:

Indicators of Central Tendency Mode Most Frequently Occurring Score Median Middle Score Mean Arithmetic Average.

Normal Distribution

Normal Distribution

Normal Distribution

Non-Normal Distribution

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

Mean  SD

Standard Error of the Mean (SEM) 68.26% ????????????????????????????????????????????????????? Number of Press-ups

Standard Error of the Mean (SEM) SD n SEM =

Mean  SEM

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

Put the data from each trial into SPSS… Week 2 Week 1

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

Move variables from here… …to here, click ok

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

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

Mean  nCI

Selected Reading Hopkins W. G. (2000) A New View of Statistics [Online] Auckland: Internet Society for Sport Science. Available at: www.newstats.org [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. 57:203-220, 2003.