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# Statistical Analysis Overview

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### Statistical Analysis Overview

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