Download Descriptive

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Quantitative Analysis:
Supporting Concepts
EDTEC 690 – Methods of Inquiry
Minjuan Wang (based on previous slides)
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Agenda
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Quick review of data
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Why analysis is necessary – beyond descriptive statistics
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The Culture data posted on BB
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Descriptive analysis vs. inferential analysis
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Review Key Concepts of Descriptive Statistics
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Inferential analysis concepts
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Types of tests – parametric and non-parametric
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What test should I use when?
Next steps for your studies
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We will help you with inferential analysis using SPSS or other
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Our Special Guests:
Types of Analysis
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Descriptive statistics
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Correlation
 Measuring a relationship
between studied variables
Inferential statistics
 Inferences from a studied
sample to a population
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Parametric analyses
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Nonparametric analyses
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What is measurement?
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Measurement: process of
assigning numbers, according
to rules defined by the
researcher.
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The numbers are assigned
to events or objects, such as
responses to items, or to
certain observed behaviors
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Correspondence between
event/objective/behavior
and number is defined by
the researcher
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Types of Measurement Scales
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Nominal
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Ordinal
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Involves order of the scores/ratings on some basis (e.g., attitude
toward the government)
Interval
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Categorization, no implied order (e.g., sex, eye color)
Unit interval is the same across the scale, doesn’t necessarily
begin at zero (e.g., time, test score)
Ratio
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Equal unit with a true zero point (e.g., the government
expenditures; birth weight in pounds)
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Let’s Practice!
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GRE test
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Celcius temperature scale
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Kelvin temperature scale
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Football jerseys
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IQ tests
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Grade Point Average
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Economic status as High, Middle, or Low
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Number of siblings
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Descriptive
Statistics
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Descriptive statistics
A
mathematical summary
of the data is required
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Paints a picture of your data
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Provides the necessary
background and foundation for
interpretation
 But
descriptive data falls
short
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A frequency count, constructing
histograms or a graph – they’re
not enough in most research
reports
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Descriptive statistics
 Describing
a
distribution of scores
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To provide information
about its location, dispersion,
and shape
 Mean, median
 Standard
mode
deviation
 Normal distribution
(i.e., bell shape or skewed)
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Shapes of distribution (single variable)
Distributions with like
central tendency (means)
but different variability
Distributions with like
variability but different
central tendency (means)
Frequency distribution--Normal Curve (Figure
12.2, p. 445)
Many statistics assume the normal, bellshaped curve distribution for scores.
50% > mean; 50% < mean
Normal curve for population (height, weight, IQ scores)
Mean=median=mode
Mean + 1SD/34.13% of the score
Mean – 1SD/34.13% of the score
Mean +/- 3SD = more than 99% of the score
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Skewed Distribution
 Non-symmetrical distribution
 Mean, median, mode not the same
 Negatively skewed (Figure 12.3, p. 447)
 extreme scores at the lower end
 Mean < median <mode
 most did well, a few poorly
 Positively skewed
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at the higher end
Mean >median >mode
Most did poorly, a few well
Colorado Mountain: Ski to the right->skew to the right
 The further apart the mean and median, the more
the distribution is skewed.
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Describing-Variability
 Standard Deviation [or dispersion] (average
distance from the mean)
1 sd includes 34% above and below mean
2 sd includes 47.5% above and below mean
3 sd includes 49.9 % above and below mean
SD chart by Kathleen Barlo
URL:
http://edweb.sdsu.edu/eet/Articles/standarddev/index.h
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Using SD in Prescribing Cereal
 As a practicing nutritionist, Dr. Green frequently
came across patient questions like "what is the
cereal that are within my diet in terms of calories
and fat grams?"
Dr. Greenly uses descriptive statistics to give advise.
Launch Cereal data
Draw frequency histogram
Fruit loop calories: SD=+2
Give it to someone who is trying to lose 10 lbs?
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Predicting Height: Normal Distribution
Mean Height
SD
Monday
67.9”
3.56”
Tuesday*
68.0”
3.6”
Both Sections
68.0”
3.5”
From this sample of 30 adults, the average height of
is 68.0 inches or 5 feet 10 inches tall and that 99%
of all adults fall in between the height of ??? And ???
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Measure of relative standing
 Z-score
One type of standard scores
Compares scores from different tests
Convert scores to z scores, average them->final index of
average performance
Z= Raw Score (X)-Mean/SD
Z score of mean = 0
 Percentiles
 The percentage of scores that fall at or below a given score
 Outliers
Example
 GRE
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Correlation (relationship between two variables)
 The
correlation
coefficient is a
measure of the
relationship between
two variables.
 It
can vary from -1.00
to +1.00. Zero
indicates no
relationship.
Describing-Relationships
 How variables are related--need at least 2
variables
 Spearman rho
coefficient correlates data that are ranked
 Pearson r
correlates data that are interval or ratio
 How does foot size correlate to GRE scores?
Scores go from +1 to -1
 More in “Correlational Research”
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Mini-Data Activity (After Spring break)
Salary Data
Culture Data
When you are
not heavily
cognitively
overloaded…..
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