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1.3 Data Recording, Analysis and PresentationInferential statisticsInferential Statistics ChecklistContent:Highlight the following to illustrate your understandingSymbols =, <, <<, >>,> normal distribution curves skewed distribution curves Significance Levels Probability criteria and use of parametric test criteria and use of specific non parametric inferential test (Mann-Whitney U test, Willcoxon Signed Ranks test, Chi Square, Binomial sign test, Spearmans Rho) Type 1 error Type 2 error Key Symbols:= equal to/= not equal to> greater than>> much greater than< less than<< much less thanKey terms:Observed valueThe number produced after the various steps and calculations for a statistical test have been carried out. Basically, the final result/numberCritical valueA value taken from a statistical test table, which must be reached in order for results to be significant. In Psychology, it is typically <0.05RanksOrder the data Distribution curvesDistribution curves are used to display the data gathered from a research study.There are three types of distribution curves:Skewed positiveNormally distributedSkewed negative1. NORMAL DISTRIBUTION CURVEThe mode, median and mean are together in the centreThe proportion of scores falling on either side of the centre is the same - 50% of the scores to the left of the centre and 50% of the scores to the right (symmetrical)Example: A researcher was looking at the time it took Charlotte and Rachel’s participant sample to complete a test. The mean time is 15 minutes, and the standard deviation is 2 minutes. Looking at the first image below, this shows that 68% of participants (-1 +1) have scores between 13 minutes and 17 minutes [2 minutes (SD) above and below 15 (MEAN)]. When we are looking at normal distributions, 95% of the data lie within the first two standard deviations of the mean. And so, if we look at -2 and +2 on the graph below, we can say 95% of the participants completed their test within 11 minutes and 19 minutes (2 standard deviations of the mean).Like any data set, there will be extreme scores. In normally distributed graphs, these are displayed in the ‘tail’ to the right of two standard deviations. These are half of the remaining 5%. So 2.5% each side. These individuals may have completed the test extremely slow or extremely fast. 2. SKEWED DISTRIBUTIONSIn normal distribution curves, all measures of central tendency lie together in the middle. However, in skewed distributions this is not the case. There is a greater spread of scores on one side (See images on page 1).Complete activity 1 on your A3 sheetHypotheses in inferential statisticsInferential statistics tell us whether what we have found is likely to be found by anyone else doing similar research. In other words, inferential statistics answer the following questions; What is the probability of us getting our results by chance? Or, have we got our results because there is a relationship or correlation between the IV and the DV?In statistical testing we aim to reject our null hypothesis. This is what we do when we can show that it is unlikely what we have found is due to chance. If this is the case, we would say our results are significant and reject our null hypothesis. We would also accept our alternative hypothesis. Whereas, if it is likely we got the results by chance, we would accept our null hypothesis, stating the results we received are non-significant, and due to chanceSignificance LevelsHow do we know if the results are significant or non-significant?Ideally, psychologists want to be 100% sure that the IV has affected the DV. However, this is rarely case and so, the most ocmmon level of significance used by psychologists is 95%. This would mean, there is a 95% certainty that the IV has affected the DVFor example: If I conducted a study that investigated the effects of a crowd on sporting performance, I would have two scores: one for a sporting performance with no crowd and one with a crowd. Let’s imagine that each participant took ten free throws in basketball. If the mean score (out of ten free throws taken) for no crowd was 8, and for crowd it was 5, we can say that there is a difference between the groups. Using an inferential statistics test tells us whether the gap is large enough to say that the IV (crowd or no crowd) has affected the results and that the results were not due to chance.If the stats test says I have a significant result then I can be 95 per cent sure that crowds have an effect on sports performance.P ValuesP = probability of the results being due to chance< = is less than0.05 = 5%P<0.05‘The probability of getting this result by chance is less than 5 times in one hundred’ This is your ‘level of significance’Complete activity 2 a, b and c on your a3 sheetProbabilityWhat is probability?Probability is the measure of how likely an event is to occur out of the number of possible outcomes. In Psychology, we use probability because we want to know what the chances of changes in the DV occurring are, to ensure the IV really did cause a change in the DV.Calculating probabilities can seem tricky at first, but once you learn the simple formula, you’ll be able to do it easily. How to calculate probabilityStep 1: Define your events and outcomesProbability is the likelihood of one or more events, divided by the number of possible outcomes.Example 1: What is the likelihood of choosing a day that falls on the weekend when randomly picking a day of the week?Event>> Picking Saturday or Sunday Number of outcomes>> 7 (days of the week)Example 2: A jar contains 4 blue marbles, 5 red marbles and 11 white marbles. If a marble is drawn from the jar at random, what is the probability that this marble is red?Event>> Picking a red Number of outcomes>> 20Step 2: Divide the number of events by the number of possible outcomesThis will give us the probability of a single event occurring. Example 1: 2 (days) divided by 7 (days)2/7 = 28.5%Example 2: five (marbles) out of 20 (marbles)5/20 = 25%Complete the following questionsTossing the coin-32512010985500If you toss a coin, what is the probability of landing on the tails side of the coin? Explain why. After the coin lands on tails five times in a row, what is the probability of getting a tail on the sixth throw? Explain why. 4095754283600-9271025908000Rolling a diceWhat is the probability of rolling a 6? Explain why.What is the probability of rolling either a 2 or a 3? Explain why. What is the probability of rolling an odd number? Explain why.4785642828120026924028956000Choosing a card from a pack of cardsFrom a pack of 52 cards, what are the chances of picking a heart? Explain why.What is the probability of choosing the queen of hearts? Explain why. What is the probability of a choosing a red card? Explain why. 3800744889500 3657600-223757NON-PARAMETRIC TESTDoes not assume the population is normally distributedAre used when distributions are non-normal00NON-PARAMETRIC TESTDoes not assume the population is normally distributedAre used when distributions are non-normalSelecting which inferential statistics to useleft279032PARAMETRIC TESTAssume that the source population is normally distributed00PARAMETRIC TESTAssume that the source population is normally distributedThere are two types of tests you can select from:45053252352417239004185703159760164121TYPES OF NON-PARAMETRIC TESTSMann Whitney U Wilcoxon Signed RanksChi-SquareBinomial SignSpearmans Rho00TYPES OF NON-PARAMETRIC TESTSMann Whitney U Wilcoxon Signed RanksChi-SquareBinomial SignSpearmans Rho026433TYPES OF PARAMETRIC TESTS:t-test00TYPES OF PARAMETRIC TESTS:t-testIf you have a distribution graph which is not normal. There are a range of non-parametric tests to use. Often, it can be confusing when to use each test. However, aspects to bear in mind when choosing the appropriate non-parametric test are:Type of Data –do the findings from the study use nominal, ordinal or interval data?Experimental Design – have you used independent measures or repeated measures design?Differences in conditions – are you exploring differences in performance, test scores, between two conditions in your experimental study?Are you looking for a relationship (or correlation) between the co-variables?Type of dataIndependent measuresRepeated measuresCorrelationNominalChi Squared testBinominal Sign TestN/AOrdinalMann Whitney U TestWilcoxon T Signed Ranks TestSpearman’s Rho Correlation CoefficientInterval RatioThese require parametric data (interval/ratio, data has to have curve of normal distribution, similar variance). For A level Psychology we treat interval ratio as ordinal so use the same tests as ordinalleft13023850085725078740003009904249329NOTE: for Wilcoxon Signed Ranks Test, Level of significance is t NOT w00NOTE: for Wilcoxon Signed Ranks Test, Level of significance is t NOT wUsing statistical testsRead over the following scenarios. Using your inferential statistics check list, identify which statistical test should be used.You should then identify three reasons why you have chosen this test. You must contextualise your answers (refer to the words in the scenario provided).SScenario 1: A psychology teacher wanted to compare the effectiveness of two A Level textbooks in making psychology easy and fun to study. The teacher decided to conduct research with students on the course to decide which new books to choose. On a piece of paper, students had to rate (out of 10, with 10 being “We love this textbook – BUY BUY BUY”) the overall likelihood of choosing the student-centred psychology textbook. Out of 12 participants, 6 of the participants gave ratings for one of the textbooks (Textbook A), and the other 6 participants gave ratings for the other textbook (Textbook B). -2563715329500Scenario 2:Psychologists were interested in knowing whether a group of students’ abilities to memorise words was because of the ear that they used to hear the words during listening tasks. In order to investigate this, participants were individually presented with an audio recording of a list of words. These were randomly presented to the left or right ear. Participants gave two sets of scores – words remembered correctly from the left ear and words remember correctly from the right ear. When the mean and standard deviation were calculated, it was found that the data was positively skewed which suggested that the data was not normally distributed. As a result, a Wilcoxon’s was used to examine the difference between each ear and to see if the difference did not occur by chance. -6760112763500Scenario 3:On a recent trip to London, a research psychologist could not help but notice the number of people walking in streets with earphones. Surprised by this one afternoon, the research psychologist decided to conduct an observation. She observed the number of people with earphones in their ears and to see if there was a difference in the frequency between male and females.-1801096794500Scenario 4:Two students wanted to examine whether their peers would be willing to share their French fries when in the school refectory. The two students wanted to know if a celebrity was sitting on their table or if students from another school were sitting on their table, would their peers be willing to share their French Fries. They hypothesised that students would be more likely to share with a celebrity. 0000Scenario 5:Fifteen students in a Psychology undergraduate course, where asked how long they have had their Social Media profile and were asked to rate, on a 5-point scale from 1= not at all to 5 =, their beliefs about whether Facebook is an effective social media tool to connect with their friends.0000Types of error:Type 1 errorType 2 errorWhen using parametric tests type ___ error is more likely to occur.Revision and RecapTask 1: Novel Situation Children’s tendency to stereotype according to traditional gender roles was observed. They were asked questions about several stories. It was assumed by the researchers that children whose mothers had a traditional role would be more likely to produce stereotyping than those whose mothers had a full time job. The maximum score was 100, indicating extreme stereotyping. Two groups were used: one with mothers who had full time paid employment and one whose mothers did not work outside the home.Mothers had full time jobMothers with no job17193263397827295835255931778168a)Write the null hypothesisb)Write what the experimental hypothesis would be for this researchc)Calculate measures of central tendency.d)Which statistical test would you use in this situation and why?Task 2 – Novel SituationPsychologists were very keen to understand whether blinking had on effect on recall of words. Participants took part in both conditions of the experiment. Each participant was instructed to blink five times in condition (1) and ten times in condition (2). The below table indicates the performance of each participant.ParticipantCondition (1) – 5 blinksCondition (2) – 10 blinks1342245453562242331516156464789138342795830107621Task 3 – Novel Situation A psychologist is interested in seeing whether there is a link between political party membership and opinion over legislation to ban smoking in cars. Opinions from 200 members of the Labour party and 200 members of the Conservative party were collected.ForUndecidedAgainstConservative6822110Labour921890Looking at the overall sample, what were the simplified ratios for?214527233503020000For banning of smoking in cars.217170241300020000Undecided.217170246380020000Against smoking in cars.What percentage of Conservatives are:217170208280020000For banning of smoking in cars.217170213360020000Undecided217170229870020000Against smoking in cars.What is the ratio of Labour supporters who are?248920205740020000For banning of smoking in cars.248920231775020000Undecided.248920248285020000Against smoking in cars.-1939022151200What is the null hypothesis for this psychological research?-1587523939500What is the experimental hypothesis?Give details of the statistical test you would conduct.-152405524500Task 4 Use the box below to choose two behavioural topics to link to design an experiment (choose 1 behaviour from column one and 1 impact on individuals from column 2).BehaviourParticipantsLocationEating sweetsFriends and non-friendsSchool playgroundPlaying games on phoneCelebrities and non-celebritiesShopping centreLending moneyCrocodiles and ChickensCanteenMemorising telephone numbersRobots and HumansLibraryLearning tongue twistersSuperheroes and non-superheroes Concert hallCreate an experimental and null hypothesisFor example; more sweets will be shared with friends than with other people in the school playground.427178388380042989539941500Imagine participants are in the specified role, for example, super heroes and non-superheroes. Would they be willing to share sweets? Collect data which should be in the form of the value of yes or no. Decide which value will be assigned positive or negative numbers. 429895501650042989521606200Which statistical test would you conduct?Create a table and calculate the observed value.4298953238500Task 5 Recently, there has been research to indicate that the number of years people have been watching TV determines whether they will become richer.21452723242600Identify the null hypothesis. 21717022479000Create a 5 point rating scale of values from 1=disagree to 5 =agree.Select 10 participants.217170615950022796522479000Collate data on years participants have been watching TV and their ratings.22796522479000Create a table of raw data.22796523558500Which statistical test would you conduct and why?22796520320000Find the critical value of the data collected.22817223588100Is your study significant or not significant? Explain your answer.Task 6 What do you remember?43307038227000Which test is used when predicting a difference for an independent measures design with ordinal/interval data?43307021907500What is the difference between Mann-Whitney and Wilcoxon tests?43307021907500Which two tests are used for nominal data?43307017653000How is Spearman’s different to the other tests?Where is a critical value found? Which two factors must be considered when choosing the correct value?43307012211000 24193538735000In which tests must the observed value be greater than the critical value in order for results to be significant?24193524574500How do we calculate degrees of freedom and why do we need to know them? ................
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