Transcript Descriptive Statistics

Analysis of Research Data
Statistical Analysis of Research
Data
Purpose of Statistical Analysis
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To summarize
To explore the meaning of deviations in data
To compare or contrast descriptively
To infer that findings from the sample are
indicative of the entire population
To examine causality
To predict
To test the proposed relationships in a
theoretical model
To infer from the sample to a theoretical
model
Elementary Descriptive
Statistics
• Univariate descriptive statistics – these
describe and synthesize data from
empirical observations
– Averages and percentages
– Frequency distributions
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Cumulative frequencies
Bar graph – nominal or qualitative
Frequency histograms – ordinal, interval or ratio
Frequency polygons – ordinal, interval or ratio
Elementary Descriptive
Statistics
– Measures of central tendency
• Mode – for nominal data – where scores fall most
frequently
• Median – for ordinal data – the point above which
and below which 50% of the scores fall
• Mean – for interval or ratio data – the sum of the
scores/the number of scores
Elementary Descriptive
Statistics
– Measures of dispersion or variability – the degree to
which subjects in the sample are similar to each other
with respect to the critical aspect – the extent of intersubject differences
• Range – for nominal data – the highest number minus the
lowest number
• Inter-quartile range – for ordinal data - the range between the
middle two quarters where 50% of scores lie
• Semi-interquartile range – for ordinal data – half of the range
of scores in which the middle 50% of the scores lie
• Variance – for interval data - how much the score varies from
the mean (the average of the sum of squares)
• Standard deviation – for interval data – the average of the
deviations from the mean (the square root of the variance)
Standard Deviations in a
Normal Distribution
Two Distributions of Different
Variability
Elementary Descriptive
Statistics
• Shapes of distributions
– Symmetrical – two halves fold over on themselves –
the normal curve. In order to compare the scores in
one sample with the scores in another, mechanisms
were developed to transform raw scores into standard
scores
– Non-symmetrical – skewed
• Positively – long tail to right (personal income)
• Negatively –long tail to left (age at death)
Examples of Skewed Distributions
Elementary Descriptive
Statistics
– Shapes of distributions
• Modality – most distributions are unimodal, but if
they have more than one mode, they are most
often bimodal – having two peaks
• Kurtosis – the degree of peakedness of the curve
– Platykurtic
– Mesokurtic
– Leptokurtic
Elementary Descriptive
Statistics
• Bivariate Descriptive Statistics – where
there are two variables
– Contingency tables – a two dimensional
frequency distribution – the frequency of two
variables are cross tabulated
– Correlation – can determine the direction of a
relationship between two variables – can
display data graphically by use of the scatter
diagram
BIVARIATE
GENDER
OBAMA
McCAIN
TOTAL
Male
43 (33.6)
85 (66.4)
128 (100)
Female
215 (52.2)
197 (47.8)
412 (100)
TOTAL
258 (52.2)
282 (47.8)
540 (100)
Various Relationships Graphed
on Scatter Plots
Elementary Descriptive
Statistics
• In a positive relationship, the scores vary together in the
same direction and the slope of the line is from the 0 point of
each variable to the upper right corner
• In a negative relationship, the scores vary inversely, in
opposite directions with the 0 of the independent variable
being at the upper left corner or high level of the dependent
variable and dropping to the lower right corner of the graph
• The most common correlational statistical technique is
Pearson’s Product Moment Correlation Coefficient. The
outcome of the formula is an “r” value which indicates the
degree of relationship between the two variables with +1
equaling perfect positive correlation and –1 equaling perfect
inverse correlation