Inferential statistics, Descriptive statistics   Remember, descriptive statistics don’t prove/disprove your hypothesis; they just describe your data because ‘Raw data’ is difficult and sometimes impossible to read/gauge. You describe your data with tables/charts/graphs showing measures of central tendency and measures of dispersion.

Key words Null hypothesis Level of measurement Observed value Probability Falsification Critical value

From the horses mouth!!!!!!!!! The learners will not be required to carry out an inferential statistics test in the assessment. However they should know the conditions necessary to carry out each test.

Intro to inferential statistics Inferential statistics allow the researcher to generalize their findings from the sample data to the larger population. They help assess the strength of the relationship between the independent (causal) variables, and the dependent (effect) variables. With inferential statistics, we are trying to reach conclusions that extend beyond the immediate data alone (i.e. our sample). For instance, we use inferential statistics to try to infer from the sample data what the population might think.

Inferential statistics Now, suppose you need to collect data on a very large population. For example, suppose you want to know the average height of all the men in a city with a population of so many million residents. It isn't very practical to try and get the height of each man. This is where inferential statistics comes into play. Inferential statistics makes inferences about populations using data drawn from the population. Instead of using the entire population to gather the data, the statistician will collect a sample or samples from the millions of residents and make inferences about the entire population using the sample. The sample is a set of data taken from the population to represent the population. Probability distributions, hypothesis testing, correlation testing all fall under the category of inferential statistics. In inferential statistics, the answers are never 100% accurate because the calculations use a sample taken from the population. This sample doesn't include every measurement from the population, and the methods use probability to fill in missing gaps. To account for this, another aspect of inferential statistics covers ways to lessen the margin of error and ways to control how much error you introduce into your calculations. This is known as statistical estimation

WHY INFERENTIAL STATISTICS? Inferential statistical tests are more powerful than the descriptive statistical tests like measures of central tendency (mean, mode, median) or measures of dispersion (range, standard deviation). Descriptive statistics analyse the findings from a sample, but inferential statistics tell you how the sample’s results relate back to the target population from which the sample was drawn. This is vital for working out whether the results support the null hypothesis or force you to reject it in favour of the alternative hypothesis. Allows us to either accept or reject our hypothesis

What inferential test will you use? Remember in ‘order for you to find out whether a test is statistically significant or did not occur by chance alone, you have to do an inferential test. Before you can choose a test, you need to know the following about your data and investigation.

What inferential test will you use? What is your level of measurement data (e.g. Nominal, Ordinal, Interval or Ration? Do you need a test of Difference, Association or Correlation? If you need a test of Difference what design are you using: Independent Group, Matched Pairs or Repeated Measures?

Difference (experiments); Tests of difference are usually experiments as they are testing a difference between conditions. Association (non experimental studies, e.g. observations, content analysis or discourse analysis). Data is always nominal as you are simply counting the frequency something occurs Correlation? When it is non experimental and you are testing a relationship/link between two variables/groups of participants.

Type of test-Difference- usually experiments as they are testing a difference between conditions They can also be non experiments (or quasi) though, e.g. when differences between the participants are being tested but they are only doing on thing, e.g. participants from the UK and participants from USA all answering a questionnaire on eating attitudes. This is not an experiment as all PP’s are doing the same thing but we are still testing a difference between PP’s from USA and PP’s from UK. Usually tests of difference will be ordinal data Tests of Difference (Experiments) Independent Group Design with data that is Ordinal, Interval/ratio Man Whitney U test Repeated Measures/Matched Pairs Design with data that is Ordinal only Sign Test Repeated Measures/Matched Pairs Design with data that is Interval/Ratio only Wilcoxan Matched Pairs Signed rank test

Association testing Association (non experimental studies, e.g. observations, content analysis or discourse analysis). Data is always nominal as you are simply counting the frequency something occurs Tests of Association When data is Nominal and in frequencies or categories Chi square Tests of Correlation Spearman’s Rho

When to use the types of test Mann-Whitney U-test is for experiments with independent groups design Wilcoxon test is for experiments with repeated measures or matched pairs design Spearman’s Rho is for correlations Chi-Squared is for analysing independent variables in categories (eg most observations) Sign test- repeated measures, using nominal data

Why are they used?- justification Spearman’s Rho - This test is used to determine if there is a correlation between sets of ranked data (ordinal data) or interval and ratio data that have been changed to ranks (ordinal data). Mann u whitney- The test evaluates whether there is a significant difference in the ranks assigned to the two IV levels. Wilcoxon- Differences between scores in the two IV levels are calculated for each participant and then ranked . The test evaluates whether there is a significant difference in the ranks assigned to the two IV levels. Chi squared- Deals with a single categorical variable - i.e. nominal level data. One-Variable Chi- square calculates the difference between expected and obtained frequencies. Tells you whether there is a significant difference, but not which IV levels are different. The sign test is a non-parametric statistical test of difference that allows a researcher to determine the significance of their investigation. It is used in studies that have used a repeated measures design, where the data collected is nominal/ordinal.

Observed values The number produced AFTER applying an inferential test. You will be given the observed value as you are not required to calculate it

Critical value Critical values are a numerical value which researchers use to determine whether or not their calculated value (from a statistical test) is significant. Some tests are significant when the observed (calculated) value is equal to or greater than the critical value, and for some tests the observed value needs to be less than or equal to the critical value.

Levels of significance This refers to the minimum probability we will accept that our results are due to chance. If it is too lenient, then our results may appear to be significant when in fact they are not. If it is too stringent, then our results may appear to be insignificant when they actually they are. In psychology, we generally aim for a significance level of __5_____%. This means that we can be ___95______% certain that our results are not due to chance. This is written as P≤__0.05_____ 5% probability is expressed as p<0.05 and if we find that the null hypothesis can be rejected we can be 95% confident of the conclusions.

Inferential statistics test Rules for significance Observed and Critical values Inferential statistics test Rules for significance Spearman's Rank Observed value of rho must be EQUAL TO or GREATER THAN the critical value for significance to be shown. Chi-Squared Observed value of X² must be EQUAL TO or GREATER THAN the critical value for significance to be shown. Sign Test Observed value of S must be EQUAL TO or LESS THAN the critical value for significance to be shown. Wilcoxon Observed value of T must be EQUAL TO or LESS THAN the critical value for significance to be shown. Mann-Whitney Observed value of U must be EQUAL TO or LESS THAN the critical value for significance to be shown.

Tests of significance Whichever test is used a value is calculated which is called the observed value.  The value then has to be compared with the critical value to determine whether the null hypothesis can be rejected and at what value.

Recap on hypothesis When we carry out a test of difference we have two hypotheses.  A null hypothesis which states that the results will be due to chance, and the experimental (alternate) hypothesis, which predicts that the results are due to the manipulation of the independent variable.   Inferential statistics tell us whether the difference between two sets of scores is significant or due to chance.  It is an academic convention that in psychology we accept the null hypothesis as the best explanation for out results unless there is a 5% probability (or less) of the results being due to chance.

When to accept/reject the null If the observed Wilcoxon value T was lower than the critical Wilcoxon value, this would have suggested that the results of the study were significant, in which the null hypothesis would have been rejected. If the observed value is higher than the critical you accept the null and reject the alternative

When to accept/reject the null If the observed Chi Squared value X² is greater or equal to the critical value of Chi Square. Then you reject the null and accept the alternative hypothesis. The results of the study are significant If the observed value is less in a chi squared then you accept the null

When to accept/reject the null Spearmans- Observed value of rho must be EQUAL TO or GREATER THAN the critical value for significance to be shown. If the observed value is less than critical value you accept the null and reject the alternative

When to accept/reject the null Sign Test Observed value of S must be EQUAL TO or LESS THAN the critical value for significance to be shown. If the observed value is more than the critical, you accept the null and reject the alternative

When to accept/reject the null Man whitney u- Observed value of U must be EQUAL TO or LESS THAN the critical value for significance to be shown. If the observed value is more than the critical, you accept the null and reject the alternative

For each test, identify Type of experimental design associated with this test When you would use this test Why you would use this test Make additional useful notes- you don’t have to calculate