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HL Psychology Internal Assessment Inferential Statistics What you should know after this PowerPoint: • A concise review of descriptive statistics • Differences between descriptive and inferential statistics. • Why we use inferential statistics in psychology • How to properly choose an inferential statistics test. • How to distinguish between various types of data. • How to test for statistical significance. Descriptive statistics provide for.. • Measure of central tendency o Gives a typical value for the data set o Tells you where the middle of the data set is • Measure of dispersion o Indicates how the data are spread out o Tells you what the rest of the data are • The aim of descriptive statistics is to give an accurate summary of the data • The wrong choice of statistic gives a distorted picture of the data • This can lead to the wrong conclusions being drawn from the data • Each measure of CT and D has its advantages and disadvantages www.psychlotron.org.uk Descriptive Statistics Measures of Central Tendency • The mean – total scores divided by the number of scores • Use it when the data are normally distributed, unskewed and there are no outliers www.psychlotron.org.uk o Adv: it uses all the values in the set, so is most sensitive to variations in the data o Dis: it can be artificially raised or lowered by an extreme value, or by skewed data Measures of Central Tendency • The median – the middle score in a range What is the median 2,3,3,4,4,4,4,5,5,6,42? • Use it when you can’t use the mean because of skew, outliers etc. www.psychlotron.org.uk o Adv: it is based on the order of the data, not their actual values, so not distorted by extreme values o Dis: however, this makes it less sensitive to variations in the data Measures of Central Tendency • The mode -most frequently occurring value • Use when dealing with frequency data, and/or where there is a clear modal value in the set www.psychlotron.org.uk o Adv: it’s the only measure suitable for summarising category/frequency data o Dis: for many data sets there is no modal value, or their may be several Calculate…. • A psychologist has obtained the following scores. Answer the questions below. • 8 1 5 5 2 7 1 1 1 4 6 8 9 9 • The range of these scores is __________________________ • The mean of these scores is __________________________ • The mode of these scores is __________________________ • The median is ______________________________________ Measures of dispersion • Range-difference between the smallest and largest value Ex 3,4,7,7,8,9,12,4,17,17,18 =18-3 =16 • Although quick and easy to calculate it is distorted by extreme values Standard Deviation • Standard deviation – a measure of the spread of scores around the mean • It is the most sensitive measure of dispersion using all available data. It can be used to relate the sample data to the population’s parameters. SD formula • Sum of all participant scores divided by the no of participants = mean • Subtract the mean from each score • Square each of these scores • Total the squared scores • Divide by one less than the total participants. This is the variance • Take the square root of the variance. Work out the SD…. • Scores – 13,6,10,15,10,15,5,9,10,13,6,11,7 Graphs • Bar chart –Shows data for categories that the researcher is interested in comparing Histogram • Shows data for all categories even those with zero value Frequency polygon/line graph • Shows two sets of data on one graph Pie charts • Show the proportion of all scores gained by various categories Inferential Statistics HL IA ONLY Inferential Statistics • With inferential statistics, you are trying to reach conclusions that extend beyond the immediate data alone. For instance, we use inferential statistics to try to infer from the sample data what the population might think. • Or, we use inferential statistics to make judgments of the probability that an observed difference between groups is a significant one or one that might have happened by chance in this study. Inferential Statistics • Thus, we use inferential statistics to make inferences from our data to more general conditions; we use descriptive statistics simply to describe what's going on in our data. What you are bring asked to do (HL IA). • An appropriate inferential statistical test has been chosen and explicitly justified. Results of the inferential test is accurately stated. • The null hypothesis has been accepted or rejected according to the results of the statistical test. A statement of statistical significance is appropriate and clear. What you are bring asked to do (HL IA). • The information you have obtained from participants takes the form of raw data. This should go into the appendices, and you should use your results to calculate descriptive statistics appropriate to your to data. • The test you choose is dependent on the level of measurement of your data and whether you used independent samples or repeated measures. Levels of Measurement • Nominal-frequency headcount; things can only belong to one category ex the no of students wearing yellow shirts. • Ordinal –data which is ranked or put in order. It is not known what the interval between each rank is ex 1st,2nd,3rd time in a swimming trial • Interval/ratio- measurement on a scale where the intervals are known and equal (ratio has a true zero point; interval can move into negs. Ex of ratio is time in secs. Levels of data: nominal • Which newspaper paper do you read regularly? • We can put these into categories. Levels of Data: ordinal • What grade did you get for each of your portfolio? • These can be put in order… highest to lowest Levels of data: interval • How quick is your reaction time? • We can measure and compare the exact time because the intervals on the ruler are equal. Inferential tests • Provide a calculated value based on the results of the investigation • This value is then compared to a critical value (statistical tables) to determine if the results are significant • In chi square, sign test, spearman’s rho the calculated value must exceed the critical value. Choosing an inferential test • Nominal data and independent measures design = Chi square test • Ordinal data and independent measures design = Mann Whitney U • Interval and ratio data and independent measures design = Unrelated T-test • Nominal data and repeated measures design =Sign test • Ordinal data and repeated measures design = Wilcoxon test • Interval or ratio data and repeated measures design = related T-test • More info: http://hs-psychology-ibhl.ismonline.org/files/2011/09/Choosing-an-inferential.pdf A directional hypothesis • Very often, we state before we test the hypothesis in which direction of the results will fall. Our hypothesis is usually directional (meaning we are predicting an increase or decrease in a time or score)and the appropriate statistical test of the hypothesis is called one-tailed. • Once you have collected the data. Decide which test you need to administer. Only one person in your group needs to work out the mathematics. Using Tests of Significance – The General procedure • Choose appropriate statistical test • Calculate statistical test • Compare the test with the critical values. These can be found in the back of the Research methods text book, or mathematics statistic books, or online. • Decide which side of the critical value your result is on. • Report the decision. Inferential statistics- indicating how significant results are. • A significant result is one where there is a low probability that chance factors were responsible for observed difference • 5% level of significance, in psychology, is acceptable (P is less than 0.05) • There is less than a 5 % likelihood that the difference was due to chance. Key Terms you will need to look up and define. Critical value Degrees of freedom P value/level Significance One-Tailed Test Two-Tailed Test Type 1 error Type 2 error Interval Ordinal Nominal