Advanced Statistics Review
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Transcript of Advanced Statistics Review
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Advanced Statistics
Review
Dr. Bhongybz '14 1
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Dr. Bhongybz '14
Why Statistics
Quantitative research will generate masses of
numerical raw data
its not in a suitable form to draw any conclusions -
its not easily digested!
It requires summarising and analysis or testing
before the research question can be answered or
hypotheses supported or rejected.
Statistical analysis is the method for achieving this.
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2 types of statistics
Descriptive Statistics
Summarise and describe the data
Inferential Statistics
which are for testing the data so we can
draw conclusions
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Descriptive statistics
Mean the average
Median mid-point, divides values in to two halves
Mode the most frequently occurring value
These are measures of Central tendency:
how the data is clustered together
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Descriptive Statistics
Range
The difference between lowest to highest value
Standard Deviation
The average deviation from the mean
These are Measures of dispersion, how spread out the data is
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Inferential Statistics
Are used to test for differences between groups, or
test for associations (correlations) in the data
It allows the researcher to test
hypotheses that these differences or associations exist
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Inferential Statistics
There are many inferential statistical
tests
They are designed for different sorts
of data, and
Different experimental designs, and
Have different rules (assumptions)
that have to be followed
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Inferential Statistics
Are divided into Parametric and Non-Parametric tests, e.g:
Chi Square = non-parametric
T-test = parametric
The parametric tests are more powerful, but
They require higher level data and have stricter rules (assumptions)
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Levels of Data
Nominal (for non-parametric) Naming, categories, e.g. gender
Ordinal (for non-parametric) Ranked data, e.g. nurses grade
Interval data (for parametric) On a scale with equal intervals, e.g.
temperature in centigrade
Ratio (for parametric) On a scale with a true zero, e.g. temperature in
Kelvin 9
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Dr. Bhongybz '14
Probability
Inferential statistical tests are reported
with a probability that the result is due
to chance alone (the alpha level)
Usually this is expressed as p 0.05
Meaning that there is a 0.05 probability
that the result was mere chance, or a
95% certainty that it was a real effect
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p =
= % chance
or:
1.0 100% 1 in 1
(dead cert!)
0.5 50% 1 in 2
(like toss of a coin)
0.05 5% 5 in 100, or 1 in 20
0.01 1% 1 in 100
0.001 0.1% 1 in 1000
Levels of Probability: The 0.05 level and below are the conventions used in research
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Hypotheses
Are used in experiments
They are statements of predicted relationships between two or more variables
Eg:
Back massage reduces anxiety
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Variables
In this example Back Massage is the INDEPENDENT variable (IV)
This is manipulated / controlled by the researcher
Anxiety is the DEPENDENT variable (DV)
This is measured to observe for changes
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Testing Hypotheses
We assume that there will be no effect or difference in our test so we actually test what is called
The Null Hypothesis
So, in our example, the null hypothesis (H0) is:
There is no difference between back massage and control groups anxiety levels
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Testing hypotheses
If the result is significant (p 0.05), the
the Null Hypothesis is rejected,
And the research (H1), or alternative
(Halt) hypothesis is accepted
Its like the principal of innocent
until proven guilty
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Statistical Significance
If we reject the null hypothesis (at say the 0.05 level) this is like saying we are 95% certain that the findings did not occur due to chance,
in other words, the measured effect is real (at least we are 95% sure)
There is still a 5% (or 1 in 20) chance we are drawing the wrong conclusion
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Type 1 & Type 2 errors
A type 1 error is a false positive - the
researcher incorrectly rejects the null
hypothesis - and declares a significant
finding
A type 2 error is a false negative when the researcher incorrectly supports the null hypothesis - and reports that there is no effect / difference
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Type 1 errors Risk of Type 1 errors is reduced by adopting a
more stringent alpha level (eg requiring p 0.01 or p 0.001 instead of p 0.05
One may wish to reduce this risk if the consequences of a false positive (type 1) error are serious, such as in a drug trial
As one reduces the risk of Type 1 errors, the risk of Type 2 errors increases, unless steps are taken to prevent this
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Type 2 errors
The best way of reducing type 2 errors is to increase the sample size in a study
This will increase the power of a study, so that it is more likely to detect differences that exist
Power Analysis is a method for determining adequate sample size
The convention is that power (beta) should be set at 0.8
that is the probability of making a type 2 error is 1-0.8 = 0.2 or 20%
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Type I and Type II Errors
Dr. Bhongybz '14 20
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Summary
There are Descriptive & Inferential Statistics
Inferential = Parametric OR Non-Parametric
Choice depends on Level of Data & Assumptions
Inferential Statistics are for testing hypotheses
Findings are reported as a probability that they are due to chance
We say they are statistically significant if p 0.05
We may make type 1 or type 2 errors when drawing conclusions
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