Understanding Statistics © Curriculum Press 2003     H0H0 H1H1

Click on each link to find out about … What Is A Statistical Test? Null & Alternative Hypotheses Significance Levels Critical Values & Tables One & Two Tailed Tests Interpreting your results

What Is A Stats Test? A way of deciding logically between two possibilities Eg “ Corries are oriented randomly ” vs “ Corries are not oriented randomly An accurate way of assessing what conclusion (if any) you can draw from your data.

What Does It Involve? You use data you ’ ve collected to do a calculation You compare what you ’ ve calculated to a number in the appropriate statistical tables You draw a conclusion

Null & Alternative Hypotheses A statistical test decides between:  The null hypothesis (H 0 ) and  The alternative hypothesis (H 1 ) You start by assuming the H 0 is true You only change your mind (and reject the H 0 in favour of the H 1 ) if you have convincing evidence. This works like a trial! You assume the accused person is innocent (H 0 ) until they are shown to be guilty (H 1 )

Choosing Hypotheses The exact wording of your hypotheses depends on the test you are using, but: Null hypothesis is usually the “ boring case ” there ’ s no difference/ no association/ no correlation Alternative hypothesis is usually what you ’ d like to show there is a difference/ association/ correlation

Significance Levels Statistical tests never give you total certainty. There ’ s always a possibility that your results could be due to chance The significance level is a way of adjusting how convincing you need the evidence to be to reject H 0 The significance level is the probability of rejecting the null hypothesis if it was actually true. Significance levels are often written as percentages eg 10%, 5%,1% The smaller the significance level,  The harder it is to get a significant result  The more sure you can be results aren ’ t due to chance

Critical Values & Tables During a statistical test, you have to compare a value you calculated from your data with a critical value This will tell you whether to accept or reject the null hypothesis Critical values come from statistical tables. Each test has its own set of tables

Reading Tables When reading tables, you have to choose the right significance level and sample size. The tables here (for Spearman ’ s Rank) show how to find the critical value with a significance level of 5% and sample size of 12

One & Two Tailed Tests For some tests, there ’ s more than one possible H 1 If you ’ re comparing grass length in fields A and B, you will have: H 0 : Grass is the same length in the two fields A 1-tailed alternative – we’re only interested in A being longer But suppose you knew before you started that field A was much more fertile? Then it would be more sensible to have: H 1 : Grass is longer in field A A 2-tailed alternative – either field could be longer The “ obvious ” alternative hypothesis is: H 1 : Grass length is different between the fields

1 or 2 tailed? 1-tailed tests can make it easier to get a significant result But should only be used if there ’ s good reason to expect that particular type of result You need to decide before getting your data whether 1 or 2 tailed is appropriate NB: You can only choose 1 or 2 tailed for some tests – details included in the slideshows on each test.

Interpreting Your Results Don ’ t just say “ Accept H 0 ” or “ Reject H 0 ” – relate it back to the actual investigation. State your significance level – a result at the 1% level is “ stronger ” than one at the 5% level Make sure any conclusions you draw from the test make geographical sense! – relate your results to theory. If you have any “ odd data ” that may have affected your results, comment on them Don ’ t say you ’ ve “ proved ” something – the results could still be due to chance.