Embed Size (px)
Citation preview
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) UnitsSeven ‘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 cdUnits 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.
Energy Intake (calories per day)
1500 2500 3500 4500 5500
Nu
mb
er
of
Pe
op
le
0
20
40
60
80
100
120
140
160 Normal Distribution
Energy Intake (calories per day)
1500 2500 3500 4500 5500
Nu
mb
er
of
Pe
op
le
0
20
40
60
80
100
120
140
160 Normal Distribution
Energy Intake (calories per day)
1500 2500 3500 4500 5500
Nu
mb
er
of
Pe
op
le
0
20
40
60
80
100
120
140
160 Normal Distribution
Energy Intake (calories per day)
1500 2500 3500 4500 5500
Nu
mb
er
of
Pe
op
le
0
20
40
60
80
100
120
140
160 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
•Performed as many press-ups as possible
Nu
mb
er o
f P
ress
-Up
s
0
20
40
60
80
100
120
140
Week 1Week 2
Mean SD
Energy Intake (calories per day)
1500 2500 3500 4500 5500
Nu
mb
er
of
Pe
op
le
0
20
40
60
80
100
120
140
160
68.26%
Number of Press-ups?????????????????????????????????????????????????????
Standard Error of the Mean (SEM)
Standard Error of the Mean (SEM)
SEM =
SD
n
Nu
mb
er o
f P
ress
-Up
s
0
20
40
60
80
100
120
140
Week 1Week 2
Mean SEM
• 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
Median & Range or IQR
Week1 2
Nu
mb
er o
f P
ress
-Up
s
0
20
40
60
80
100
120
140
160
180
200
Put the data from each trial into SPSS…
Week 1Week 2
Select ‘Analyze’, ‘GLM’, ‘Repeated Measures’…
Move variables from here…
…to here, click ok
Tests of Within-Subjects Effects
Measure: MEASURE_1
60.062 1 60.062 49.830 .000
60.062 1.000 60.062 49.830 .000
60.062 1.000 60.062 49.830 .000
60.062 1.000 60.062 49.830 .000
8.438 7 1.205
8.438 7.000 1.205
8.438 7.000 1.205
8.438 7.000 1.205
Sphericity Assumed
Greenhouse-Geisser
Huynh-Feldt
Lower-bound
Sphericity Assumed
Greenhouse-Geisser
Huynh-Feldt
Lower-bound
SourceWEEK
Error(WEEK)
Type III Sumof Squares df Mean Square F Sig.
ANOVA Output
nCI =
MSE
n[criterion t (df)]
t – Distribution TableCritical t-ratioDegrees of Freedom
12345678
12.714.303.182.782.572.452.372.31
(Google Search)
Nu
mb
er o
f P
ress
-Up
s
50
55
60
65
70
Week 1Week 2
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.
