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1. DATA ANALYSIS AND REPORTING ON INVESTIGATIONS Probability and significance 2. <ul><li>Probability: a numerical measure of chance. It represents how likely…
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  • 1. DATA ANALYSIS AND REPORTING ON INVESTIGATIONS Probability and significance
  • 2. <ul><li>Probability: a numerical measure of chance. It represents how likely it is that something will happen. </li></ul><ul><li>We deal with probability because when we analyse our results we are interested in how likely it was that our results are due to chance. </li></ul>
  • 3. PROBABILITY <ul><li>Probability, or p, is expressed as a number between 0 and 1 </li></ul><ul><li>0 means an event wont happen </li></ul><ul><li>1 means that an event defintely will happen. </li></ul><ul><li>The reason it is between 0 and 1 is the way that it is calculated. </li></ul><ul><li>To calculate the probability that a particlur outcome will occur, it has to be divded by the number of possible outcomes. </li></ul>
  • 4. Probability = Total number of outcomes in which X happens Total number of possible outcomes
  • 5. <ul><li>E.g. heads and tails </li></ul><ul><li>Probability of getting a head </li></ul><ul><li>One divided by two = .5 </li></ul><ul><li>Because only two possible outcomes. </li></ul><ul><li>We do look at conditional probability: this is the probability of an event if something else occurs. </li></ul><ul><li>There is a chance anyone can develop lung cancer. </li></ul><ul><li>The greater probability is conditional upon smoking. </li></ul>
  • 6. E.G <ul><li>P=1 if something always happens, you pick a joker out of a pack of jokers. </li></ul><ul><li>P=0 a joker out of a deck of cards with no jokers. </li></ul><ul><li>P=.5 heads or tails </li></ul><ul><li>P=.25 picking a diamond card from a pack of 52 playing cards. </li></ul>
  • 7. STATISTICAL SIGNIFICANCE <ul><li>We try to generalise from sample to populations. </li></ul><ul><li>But samples are prone to error. </li></ul><ul><li>The role of statistical tests is to find out how likely it is that what we have found I our sample accurately reflects what happens in the population. </li></ul>
  • 8. <ul><li>When researchers measure a behavior, they often compare groups to determine whether they differ on that behavior. The ultimate goal is to determine whether the difference would occur if the measurements were administered a second time, or whether the difference is accidental and not likely to recur. The degree of reliability relates to the concept of significance level. </li></ul>
  • 9. <ul><li>The significance level refers to how likely it is that an error (that is, a wrong decision about whether the groups differ from one another) would be made. Psychologists generally accept a 5 percent error rate as reasonable. In order to decide whether differences are reliable, psychologists conduct statistical tests that provide a measure of confidence in their conclusions. This area of statistics is called inferential statistics because psychologists draw inferences, or conclusions. </li></ul>
  • 10. <ul><li>In psychology the level of significance is generally set at 0.05 or 5 percent. </li></ul><ul><li>This is expressed as p=0.05 </li></ul><ul><li>P is probability: it is the likelihood of getting the findings if the null hypothesis is true. </li></ul><ul><li>Anything less than 0.05 is described as significant; it is unlikely that the null hypothesis is true. </li></ul><ul><li>Anything above 0.05 is not significant as we can’t reject the null hypothesis. </li></ul>
  • 11. <ul><li>Or more clearly, for any particular test, the significance level sets the maximum acceptable probability of rejecting the null hypothesis (because the difference in the data is large), when in fact it is true and should not be rejected. </li></ul>530
  • 12. <ul><li>The choice of 0.05 as the normal level of significance in psychology is designed to balance the risk of type 1 and type 2 errors. </li></ul><ul><li>When we do a test and find that the p value is less than our level of significance we reject the null hypothesis. </li></ul><ul><li>We accept the alternative hypothesis that a variable had an effect on another or that there is a relationship. </li></ul><ul><li>However </li></ul>
  • 13. HOWEVER <ul><li>If there is actually no such effect or relationship we have made a type 1 error. </li></ul><ul><li>Type 2 errors are in the other direction. When we do a test and find a p value that is greater than our level of significance we accept the null hypothesis. We reject the experimental/alternative hypothesis and suggest that there is no relationship or effect of the variable. However, if there is an effect/relationship then we have made a type 2 error. </li></ul>
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