Probability, Significance and the Sign Test

• inferential testing

  • statistics can be descriptive (graphs and averages) and also inferential (statistical tests)
  • we use statistical test to work out the probability of whether a set of data could have occurred by chance
  • we need to make sure our difference between the samples is big enough to be of significance
  • researchers are trying to falsify the null hypothesis
• p-values

  • p-values are a measure of whether the results happen by chance
  • before analysis, we set a level of significance, which acts as a threshold our data needs to meet before we consider it significant (minimum standard is the 5%)
  • at the 5% level, the calculated p value must be <0.05
  • if our calculated p <0.05, we can say that there is a les than 5% risk that the results occurred due to chance
  • this also means that we are 95% certain that the results did not occur due to chance and therefore there is a genuine effect/difference between groups
  • if p is not less than the specified value we fail to reject the null and therefore can't conclude that there is a genuine effect
• type 1 error

  rejecting the null when it's true (saying there is a significant result when there isn't)
• type 2

  • failing to reject the null when it's false (saying there is not a significant result when there is)
• data distribution

  • a normal distribution is symmetrical
  • sometimes data/infrequencies are not symmetrical (skews)

  
• the sign test

  • used when looking for a difference between conditions
  • used for paired or related data
  • used for nominal data
• process for using the sign test

  1. state hypotheses
  2. record the data and work out the sign - record a minus next to those who score happier before the holiday and a plus to those who are happier after
  3. find a calculated "S" by taking the lower value
  4. find a critical value of S (total number of participants who changed score +/-) - check this number on the critical value table. This has to be equal to or lower than the S value
  5. check the results are in the right direction (are their more positives or negatives)
  6. conclude