introduction of statistical testing

• the sign test: we are going to begin w/ the simple statistical test, the sign test there are 3 things you need to know: when it is appropriate to use a sign test, how to do the sign test and how to report the conclusion that can be drawn
• when to use a sign test: this is a test that is used when looking at paired or related data
• when to use a sign test: the 2 related pieces of data could come from a repeated measures design i.e. the same person is tested twice
• when to use a sign test: the sign test can also be used w/ matched pairs design because the participants are paired and therefore count, for the purposes of statistics as one person tested twice
• how to calculate the sign test: lets imagine a study where we wanted to know whether people were happier after they had a holiday, to do this we ask people to rate their happiness on a scale of 1-10 where 1 is very unhappy and 10 is very happy
• how to calculate the sign test: they do this before going on holiday and then do it again 2 weeks after they return (we wait 2 weeks for the initial euphoria of the holiday to wear off)
• step 1: state the hypothesis = this is our hypothesis, people are happier after going on holiday than they were before hand, this is a directional hypothesis and therefore requires a non-tailed test if the hypothesis was non-directional then a two-tailed test is used, this will be clear later
• step 2: record the data and work out the sign = record each pair of data and record a minus (-) for happier before and plus (+) if happier after e.g. happiness before 6, happiness after 7 the difference from after-before is 1 so this means is a + sign
• step 3: find a calculated value = S is the symbol for the test statistics we are calculating, it is calculated by adding up the pluses and adding up the minuses and selecting the smaller value, in our case there are 10 pluses and 3 minuses and 1 zero, therefore the less frequent sign is minus so S = 3 this is called the calculated value because we calculated it
• step 4: find critical value of S = N = the total number of scores (ignoring any 0 values), the hypothesis is directional therefore a one-tailed test is used
• step 4: find critical value of S = now we use the table of critical values and locate the column headed 0.05 for a 1 tailed test and the row which begins w/ our N value, for a one-tailed test the critical value of S = 3
• calculated value of S must be equal to or less than the critical value in this table for significance to be shown
• step 5: is the result in the right direction? = if the hypothesis is directional we have to check that the result is in the expected direction, in this case we expect people to be happier afterwards and should therefore have more pluses than minuses, this was the case and therefore we can accept the hypothesis
• how to report the conclusion that can be drawn: if the calculated value is equal to or less than this critical value our result is significant, in our case it is significant
• how to report the conclusion that can be drawn: as the calculated value is significant we can conclude that people are happier after going on holiday than they were beforehand
• how to report the conclusion that can be drawn: but wait - how certain are we that this is true? a statistical test only gives the probability that a particular sat of data did not occur by chance
• how to report the conclusion that can be drawn: the level of significance we selected was 0.05, this means that there is a 0.05 or 5% probability that the result would have occurred even if holidays had no effects (0.05 is 5/100 or 5%)
• how to report the conclusion that can be drawn: sometimes researchers wish to be more certain and use 0.01 e.g. if testing the effect of a drug on treating a disease
• when looking up critical values a 'one-tailed test' is used for a directional hypothesis - when you look at a one-tailed cat you know which direction it is going, a two-tailed cat goes in both directions (non-directional hypothesis)