Statistics 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 There are 4 levels of data There are 4 levels of data You need to know which level of data you are dealing with in order to select the right statistical test You need to know which level of data you are dealing with in order to select the right statistical test

Nominal Level The data can be counted into categories, e.g. there are 4 men and 4 women in the room There were 8 brown horses and 1 white one!

Ordinal Level Results are put in order, they are ranked. E.g. we could rank the place that each horse came in a race

The other 2 levels 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) 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 (no minus). Ratio: This is like interval data except the scale has a meaningful value of zero. E.g. time and length (no minus).

Why do we need to conduct statistical tests? significance Statistical tests tell us the significance of a set of findings- did the IV really effect the DV or were the findings just 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. We need to use inferential statistics to tell us if the result that we have found is due to chance or not. The minimum accepted level of probability commonly used in psychology is 5%, this is represented as 0.05 The minimum accepted level of probability commonly used in psychology is 5%, this is represented as 0.05 If the level of significance achieved is equal to or less 0.05 than the results are said to be significant i.e. not just a fluke. If the level of significance achieved is equal to or less 0.05 than the results are said to be significant i.e. not just a fluke. This would mean that we are 95% sure that the IV caused the change in the DV This would mean that we are 95% sure that the IV caused the change in the DV However there is still a 5% chance it didn’t! However there is still a 5% chance it didn’t!

Probability: As a percentage 20% as a proportion: a 1 in 5 chance. As a percentage 20% as a proportion: a 1 in 5 chance. But 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 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. 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 Remember the more stringent (lower) the level of significance you set the more significant the results are 1% is more significant than 5% 1% is more significant than 5%

Observed value: Every time you perform a statistical test you get an OBSERVED VALUE. Every time you perform a statistical test you get an OBSERVED VALUE. This observed value is also known as the calculated value because it is the one you calculated. This observed value is also known as the calculated value because it is the one you calculated. You then have to compare this observed value to a table of CRITICAL VALUES to see of your results are significant or not. 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 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. 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” P is used to represent “the probability that is due to chance” > =means greater than > =means greater than < =means less than < =means less than ≥ means greater than or equal to. ≥ means greater than or equal to. ≤ means less than or equal to. ≤ means less than or equal to. SO……………… SO……………… P < 0.05 means that the probability that the result is due to chance is less than 5%.

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 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: These can occur because: Level of probability accepted is either too lenient (too high) or too stringent (too low) Level of probability accepted is either too lenient (too high) or too stringent (too low)

Type 1 and type 2 errors Type 1 error: Type 1 error: Occurs when we conclude that there IS a significant difference when there is NOT 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 This can happen if the accepted level of probability is set TOO LENIENT Significance level set at 20% Significance level set at 20% Type 2 error: 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: You must decide the following: Are you trying to find out if your samples are related (correlate) or different? 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 design you have used- related, non related, matched pairs What level of measurement you have used. What level of measurement you have used. You can use the following table to help decide: You can use the following table to help decide:

DesignNominal Ordinal, interval, ratio Correlation/association Chi-square test of association r Independent measures Chi-squared test of independent samples u Repeated Measures Sign Test t What test to use?

Test your understanding! Using your newly found knowledge identify the test that would be suitable for the following: 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 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 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 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 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 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 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 in which reaction time was tested using an independent subject design

An experiment with nominal data and an independent groups 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 = 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 = 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 =– 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 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 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 An experiment in which reaction time was tested using an independent subject design = Mann- Whitney U test

Test your understanding Answer the questions on the handout Answer the questions on the handout