D a t a A n a l y s i s

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D a t a A n a l y s i s C o n c l u s i o n
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Ok so now that you have

• Worked around the clock
• Harassed some unsuspecting people
• Beat the stress
• Collected the data
• And you are ready to write the Report
• But wait!
• How do you present your data?

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Content

• Ways of representing data (recapitulation)
• Error and Statistical Analysis
• Drawing conclusions
• -- correlation vs causal effect
• -- correlation and significance
• Presenting your analyses

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Ways of representing data

• Line graphs
• Bar charts
• Pie charts
• Dot plots and Box Plots
• Tables
• Annotated diagrams

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Statistical and Error Analysis

• Why do this
• Evaluate the appropriateness
• of the sample size, methodology and
• instrumentation of the experiment.

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Statistical and Error Analysis

• (2) Helps to determine if your results are
• VALID depends on your
• sampling size, appropriate
• instrumentation and statistical
• treatment
• RELIABLE consistency and
• reproducibility over time, over
• instruments and over groups of
• respondents.

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Statistical Analysis

• One day there was a fire in a wastebasket in
• the Deans office and in rushed a physicist, a
• chemist, and a statistician.
• The physicist immediately starts to work on how
  much
• energy would have to be removed from the
• fire to stop the combustion.
• The chemist works on which reagent would have to
  be
• added to the fire to prevent oxidation.
• While they are doing this, the statistician is
  setting
• fires to all the other wastebaskets in the
  office. What
• are you doing? they demanded.
• Well to solve the problem, obviously you need a
  large
• sample size the statistician replies.

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Statistical Analysis When to apply it?

• When experiments involve living
• organisms (eg. Bacteria, rats, yeast)
• Living organisms respond differently even
  under the same conditions, hence there will be
  variability. In this case, statistical analysis
  is necessary.

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Statistical Analysis For small sample sizes

• Simple dotplots
• http//exploringdata.cqu.edu.au/dotplots.htm
• Displays the shape, location and spread of the
  distribution, as well as showing evidence of
  clusters, granularity and outliers.
• Easy to construct.
• A particularly valuable tool for the statistics
  student who is working without technology.

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Small sample sizes dot plots
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Small sample sizes dot plots
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Statistical Analysis For large sample sizes

• Draw a bar frequency distribution
• Determine the mean, median, standard deviation

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Statistical Analysis For large sample sizes

• Mean obtained by adding
• together each item/value
• and dividing by the total
• number of items/value
• There are 12 people in a group.
• Their ages are 26, 26, 27,28, 29,
• 30, 30, 31, 32, 33, 34, 34.
• Mean age (26 26 27 34) / 12
• 30

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Statistical Analysis For large sample sizes

• Median also known as the middle
• value.
• Their ages are 26, 26, 27,28, 29,
• 30, 30, 31, 32, 33, 34, 34.
• Median is 30.
• Odd number of values, the middle value is the
• median.
• Even number of values, the median is the
• average of two middle numbers.

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Statistical Analysis For large sample sizes

• Standard deviation reflects the
• spread and the degree to which the
• values differ from the mean.

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Statistical Analysis For large sample sizes
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Statistical Analysis Hypothesis Testing

• Used to determine if your hypothesis is
• correct.
• Basic outline of procedure
• State clearly your independent and dependent
  variables
• Show how you maintained the control variables
• Highlight key points of your research methodology
• Provide evidence that support (or do not support)
  
• your hypothesis.
• -- Graphs, pictures, charts.
• -- Highlight points concisely.

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Statistical Analysis Use of Error Bars

• For determining appropriate instrumentation
• Way of representing the uncertainty in your
  readings on your graph

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Statistical Analysis Use of Error Bars

• (1) Determine the uncertainty in each
• reading due to random errors
• incurred via instrument and human factors.

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Statistical Analysis Use of Error Bars
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Statistical Analysis Use of Error Bars
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Statistical Analysis Use of Error Bars
XY Error Bar Plots
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Drawing Conclusions

• When we have 2 variables A and B,
• Correlation When A and B regularly occur
• together
• Cause and Effect When A is the cause of B
• Correlation is NOT equal to Cause and
• Effect!!

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Drawing Conclusions

• Example 1
• Some years back, some researchers
• dug up the graves of about 200
• people. The tibia length (leg bone)
• was measured and compared with
• the ages of the people. It was
• concluded that shorter people live for
• a shorter period of time.
• Is this Correlation or Cause and Effect?

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Drawing Conclusions

• Example 2
• A certain scientist used chemicals to induce
  breast
• cancer in 3 groups of rats.
• Group 1 Rats which never conceived.
• Group 2 Rats which conceived but had abortions.
• Group 3 Rats which gave birth to baby rats.
• The results showed that the highest number of
  rats in
• the second group developed breast cancer.
• Is this correlation or cause and effect?

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Dealing with Anomalous Results

• What are anomalous results?
• These are results that do not fall
• within the line of best fit.
• Sometimes, they deviate a lot
• from the line of best fit.

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Dealing with Anomalous Results
Anomalous result
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Anomalous results occur through

• Systematic error
• (also called calibration error. A scales
  measurements are consistently different from the
  true values.)
• Human error
• -- during handling
• -- parallax error
• Mutations (in biological specimen)

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How do we remedy the situation?

• Improve experimental procedures
• Identify main sources of error
• (instrument, human, limitations of
  measurements)