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Statistical Analysis Overview

Statistical Analysis Overview






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    Statistical Analysis Overview Statistical Analysis Overview Presentation Transcript

    • Statistical Analysis A Quick Overview
    • The Scientific Method
      • Establishing a hypothesis (idea)
      • Collecting evidence (often in the form of numerical data)
      • Analysing the evidence (using statistical and other techniques)
      • Accepting / rejecting the hypothesis, coming to conclusions and providing explanation
      • Evaluating the process and making recommendation for the future
    • Basic Stuff
      • ‘ X-bar’ is the mean
      • ‘ n’ is the number in the sample (sample size)
      • ‘ ∑ x’ is the “sum of”, in this case x (in other words add up all the individuals in the sample)
    • The Null Hypothesis
      • The opposite of a hypothesis (in other words that there is no relationship between variables)
      • Thus, rather than prove the hypothesis we disprove the null hypothesis
      • If we cannot accept our null hypothesis then it is rejected and an alternative hypothesis can be accepted
    • Choosing a Method
      • The statistical method chosen will largely depend on what type of test you need e.g. a test of association, a test of difference, probability testing, diversity, degree of clustering etc.
      • Other factors such as sample size, data type (categorical vs. ordinal) and distribution are also important
    • Normal Distribution
      • If a set of continuous variables is plotted against frequency the result is likely to be a belled shaped curve called the ‘normal’ curve
      • The curve suggests that most individuals are aggregated around the average or mean (which in theory should be the middle of the curve)
      • Thus, 68.2 % lie within 1 standard deviation, either side of the mean, 95.4% are clustered within 2 standard deviations etc. (the standard deviation is calculated using a formula and gives an indication of the reliability of the mean)
    • Significance and Confidence Limits
      • Significance concerns the reliability of the data and is expressed as a percentage value
      • The 95% level of significance is usually appropriate for field data
      • This means that only 5 times out of 100 would this data (results) occur by chance
      • In significance tables the 95% and 99% levels are indicated by 0.05 and 0.01 (i.e. 5% and 1% likelihood of the data occurring by chance)
      • If the calculated value exceeds the theoretical (critical) value then the value is significant
      • Thus we can say that we are confident, at the 95% or 99% level, of the reliability of the data
    • So where do we go from here?
      • Take the data
      • Check for normal distribution by plotting a frequency graph.
      • 2. Take each hypotheses in turn
      • There is a positive correlation between Place Utility and happiness (Subjective appreciation of life ).
      • There is a significant difference between the happiness (subjective appreciation of life) of residents in two contrasting areas of Bratislava.
      • 3. Use the flow chart to determine the appropriate test
      • 4. Scatter the graphs and crunch the numbers
      • 5. Test for significance
      • 6. Draw your conclusions about the relationships and associations