Advanced Statistics

Review

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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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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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Dr. Bhongybz '14

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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Dr. Bhongybz '14

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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Dr. Bhongybz '14

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

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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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