Statistics
Descriptive
Graphs charts frequency count mean median mode
range variability standard deviation
Analytical, these tests
use a statistical test to give a p value
Correlation studies, Positive correlation, negative
correlation, no correlation
Association, causal, non-causal
Descriptive Statistics
Measures of central tendency
Sample averages, (arithmetical mean)
Find the
mean of 15.3 17.8 13.2
14.0 19.9 14.9
Median, the value at which half the measurements in a sample lie below and which
the other half lie above.
Find the
median of 15.3 17.8 13.2
14.0 19.9 14.9
19.7 2.1 14.97
21.0
(Hint - try making up a line plot)
If you have an even number of
measurements take the mean of the two middle values.
Find the
median of 12.0 15.3
17.8 13.2 14.0
19.9 14.9 19.7
2.1 14.97 21.0
Mode, the result that
occurs most often
What is the
mean number of legs owned by humans in the
Find the
mode of the following data
12.0
15.3 17.8 13.2
14.0 12.0 14.9
19.7 2.1 14.97
21.0
Data dispersal, describes the range of the results, the scatter of data.
Range = (highest measurement) -
(lowest measurement)
Find the
range of the following data
a. 10.3 10.7 11.6 14.8
14.7 14.9
b. 12.6 12.7
12.8 12.9 13.2
13.3
c. 10.3 12.9
13.0 13.1 13.2
14.9
What is the
difference between sample a and c?
Does the
range indicate this difference?
Sample standard deviation
To give a sort of average distance of
the measurements from the sample mean
However average distance from the mean
of all data is always zero
-1.0 + 0 + 1.0
3
So the deviations from the mean are
squared, this gets rid of the minus signs.
Therefore standard deviation form the
mean is described as:
Find the SD of the following
data
a. 10.3 10.7
11.6 14.8 14.7
14.9
b. 12.6 12.7
12.8 12.9 13.2
13.3
c. 10.3 12.9
13.0 13.1 13.2
14.9
(Hint, make up columns under these
headings)
x x x-x (x-x)
The larger the SD the greater the
average distance of a data point from the mean. Therefore this is a more
sensitive measure of scatter than the range.
Frequency distribution
The number of times each event occurs
is counted or the data are grouped and the frequency of each group reported.
Normally
reported as a histogram or line graph.
Normal distribution
What is
meant by normal distribution?
Skewness
Distribution curves may show skewness. Positive skewness is
biased towards the left, ie. the mean is to the right
of the median eg. global
income
Percentile
Percentile represents the percentage
of cases a score exceeds, ie 90th percentile exceeds
all but 10% of cases. The median is the 50th percentile
Univariate and bivariate
Univariate statistics
consider one variable at a time
More commonly in research the
relationship between two variables is considered
In theory there are an infinite number
of "variates"
Inferential Statistics
To what degree are sets of variables
associated, eg. poor
correlation, moderate correlation, strong correlation.
In what way
does association indicate causality?
What is
meant by the following terms? Also what does each indicate?
Positive
correlation
Negative
correlation
No
correlation
P = Probability
This value indicates the degree of
association between two sets of variables.
1 = no correlation at all
0.5 = 50/50 chance of association
0.25
= 75% chance of
association
0.1 = 90 % chance of association
0.05 = 95%
chance of association
0.01 =
Association is significant at p = 0.05 Association is highly significant at p
= 0.01
P values are reached by using an
inferential statistical test.
Critiquing
Criteria for Statistics
Perhaps the most important application
of this knowledge to you will be to allow you to analytically critique
published research. This can be done by addressing the following points.
Are appropriate descriptive stats
used? What are the levels of
measurement?
Is the sample size adequate? What descriptive statistics
are given?
Are the descriptive statistics used
appropriate to the measurement of each variable?
Is there summary statistics for the
major variables?
Is there enough information to allow
you to judge the results?
Are results clearly and completely
stated?
Are statistics, tables and graphs
consistent with the text?