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##### Statistics

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**Statistics **Data measurement, probability and statistical tests**Learning Aims**By the end of this session you are going to totally ‘get’ levels of significance and why we do statistical tests!**Levels of measurement**• These are quantitative measures of data which are of extreme importance when conducting statistical tests • There are 4 levels of measurement**Also known as levels of data**• Nominal: Counting into categories, e.g. there are 4 men and 4 women in the room • Ordinal: Results are put in order, they are ranked. E.g. we could rank the place that each horse came in a race**Levels of measurement**• Interval: Data is defined as being a specific measure, this can be measured on an instrument, there are equal intervals between each piece of data. E.g. We can record the exact temperature using a thermometer. (can be minus) • Ratio: This is like interval data except the scale has a meaningful value of zero. E.g. time and length.**Why do we need to conduct statistical tests?**• Statistical tests tell us the significance of a set of findings- did the IV really effect the DV or were the findings a fluke?! • The more significant a finding is the more effect the IV had on the DV**Probability:**• We need to use inferential statistics to tell us if the result that we have found is due to chance or not. • To establish if our results are reliable we have to look at the probability of a result being due to chance or not. • The minimum accepted level of probability commonly used in psychology is 5%, this is represented as 0.05. • If the level of significance achieved from a test is equal to or less 0.05 than the results are said to be significant. • This would mean that we are 95% sure that the IV caused the change in the DV**Probability:**• Can be expressed as: • A proportion: a 1 in 5 chance. • As a percentage: 20% • More commonly expressed as a decimal in psychology: 0.2. • In psychology: 10%=0.10, 5%=0.05, 1%=0.01 and 0.1%=0.001 • To go from % to decimal divide by 100, move decimal place 2 spaces to the left. • Remember the more stringent (lower) the level of significance you set the more significant the results are**Observed value:**• Every time you perform a statistical test you get an OBSERVED VALUE. • This observed value tells you the extent to which your results are valid, you then have to compare this observed value to a table of CRITICAL VALUES to see of your results are significant or not. • To be significant the observed value should be greater or less than the critical value depending on the type of test • Note that there will be a different table of values for different statistical tests.**Interpreting results:**• Usually in psychology if the results are significant it means that the probability of the result being due to chance is 5% or less • P<0.05 means the results are significant- so we would accept the experimental hypothesis and reject the null hypothesis**Interpreting results:**• P is used to represent “the probability that is due to chance” • > =means greater than • < =means less than • ≥ means greater than or equal to. • ≤ means less than or equal to. SO……………… P<0.05 means that the probability that the result is due to chance is less than 5%.**Test your understanding**• Answer the questions on the handout**Type 1 and type 2 errors:**• The 5% level of significance has been accepted as it represents a reasonable balance between the chances of making a type 1 or type 2 error • These can occur because: • Level of probability accepted is either too lenient (too high) or too stringent (too low)**Type 1 and type 2 errors**• Type 1 error: • Occurs when we conclude that there IS a significant difference when there is NOT • This can happen if the accepted level of probability is set TOO LENIENT • Significance level set at 20% • Type 2 error: • Occurs when we reject the experimental hypothesis and accept the null when there IS a difference • This can happen if the probability level is TOO STRINGENT • Significance level set at 1%**Deciding on a statistical test**• You must decide the following: • Are you trying to find out if your samples are related (correlate) or different? • What design you have used- related, non related, matched pairs • What level of measurement you have used. • You can use the following table to help decide:**Test your understanding!**• Using your newly found knowledge identify the test that would be suitable for the following: • An experiment with nominal data and an independent groups design • Ordinal data on both measures in a study to see if two measures are associated • An experiment with and independent groups design in which the DV is measured on a ratio scale • A study using a correlational technique in which one measure is ordinal and the other is ratio.**A study testing an association using a nominal level of**measurement • An experiment in which all participants were tested with alcohol and without alcohol on a memory test • An experiment in which reaction time was tested using an independent subject design**An experiment with nominal data and an independent groups**design = chi-squared test • Ordinal data on both measures in a study to see if two measures are associated = Spearman’s rank correlation • An experiment with and independent groups design in which the DV is measured on a ratio scale = Mann-Whitney U test**A study using a correlation technique in which one measure**is ordinal and the other is ratio =–Spearman’s rank • A study testing an association using a nominal level of measurement = Chi-Square test of association • An experiment in which all participants were tested with alcohol and without alcohol on a memory test = Wilcoxon’s T test • An experiment in which reaction time was tested using an independent subject design = Mann-Whitney U test