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  1. QA

  2. Program • Først indløbne spørgsmål • Derefter er ordet frit • Own laptops in the exam: Rules do not say anything about this, but specify printed aids and PC – so expect this is not permitted. Prepare for this.

  3. Rules for the use of PCs at exams: • http://www1.itu.dk/sw118342.asp#516_92142 • Rules for DEDA exam specially: • http://www1.itu.dk/graphics/ITU-library/Intranet/Uddannelse/Eksamen/PC-regler/Regler%20for%20brug%20af%20PC%20ved%20eksamen%20i%20Experimental%20Design%20and%20Analysis.pdf

  4. Multiple choice sektionen: • Der kan være flere svarmuligheder til spørgsmålene. • Der kan være flere svarmuligheder på 0+ af spørgsmålene

  5. Q26 i eksamen: Gennemgang • 26A) Work out the formula (algorithm) for the linear regression between the two variables. • Løsning: enten beregne manuelt eller sæt data ind i SPSS

  6. Using SPSS to obtain scatterplot withregression line: Analyze > Regression > Curve Estimation... ”constant" is the intercept with y-axis, "b1" is the slope”

  7. Correlation • Alle linear regressionformler har udseendet: • Y = a + bx --- dvs: (med tallene beregnet i SPSS) • Y = 0.602 + 1.322x • 26B) Using your regression line formula, predict how many hours per week a person installing 50 games would spend playing them. • Løsning: Sæt tallene ind i formlen. Hvis vi bruger ovenstående: • Y = 0.602 + 1.322*50  Y = 66.702 timer

  8. Scatterplot med regressionslinie

  9. 26C) Is the formula for the regression line the same if we put “number of games installed” on the Y-axis and “hours per week played” on the X-axis? •  Nej – husk at regression af X on Y ikke er det samme som regression af Y on X – der vil være en lille smule forskel

  10. Linear regression • To predict Y from X requires a line that minimizes the deviations of the predicted Y's from actual Y's. • To predict X from Y requires a line that minimizes thedeviations of the predicted X's from actual X's - a different task (although somewhat similar)! • Solution: To calculate regression of X on Y, swapthecolumnlabels (so that the "X" values are now the "Y" values, and vice versa); and re-do the calculations. • So X is now test results, Y is now stress score

  11. Regression lines for predicting Y from X, and vice versa: Y on X: predicts stress score, given knowledge of test score 120 X on Y: predicts testscore, given knowledge of stressscore 100 80 test score (Y) 60 40 20 0 0 10 20 30 40 50 n.b.: intercept = 55 stressscore (X)

  12. What is the difference between ordinal and interval data?? What kind of data are ratings? • Ordinal data fortæller os ikke noget om distancen imellem to målinger. Vi ved at ”1” er før ”2” men ikke hvor meget afstanden faktisk er. • I interval data er afstanden mellem målepunkterne konstant, men der er ikke et sandt nulpunkt • Ratings – ratings er vist bare et udtryk. Kig på hvilke karakteristika måleenheden der bliver brugt har. F.eks. ”ratings on a scale from 0-50” – jamen så er det intervaldata.

  13. Measurement • Values are measureable • Measuring size of variables is important for comparingresults between studies/projects • Different measures provide different quality of data: • Nominal (categorical) data • Ordinal data • Interval data • Ratio data Non-parametric Parametric

  14. Measurement • Nominal data (categorical, frequency data) • When numbers are used as names • No relationship between the size of the number and what is being measured • Two things with same number are equivalent • Two things with different numbers are different

  15. Measurement • E.g. Numbers on the shirts of soccer players • Nominal data are only used for frequencies • How many times ”3” occurs in a sample • How often player 3 scores compared to player 1

  16. Measurement • Ordinal data • Provides information about the ordering of the data • Does not tell us about the relative differences between values

  17. Measurement • For example: The order of people who complete a race – from the winner to the last to cross the finish line. • Typical scale for questionnaire data

  18. Measurement • Interval data • When measurements are made on a scale with equalintervals between points on the scale, but the scale has notrue zero point.

  19. 1 2 3 4 5 6 7 8 9 -4 -3 -2 -1 0 1 2 3 4 Measurement • Examples: • Celsius temperature scale: 100 is water's boiling point; 0 is an arbitrary zero-point (when water freezes), not a true absence of temperature. • Equal intervals represent equal amounts, but ratio statements are meaningless - e.g., 60 deg C is not twice as hot as 30 deg!

  20. Measurement • Ratio data • When measurements are made on a scale with equal intervals between points on the scale, and the scale has a true zero point. • e.g. height, weight, time, distance. • Measurements of relevance include: Reaction times, numbers correct answered, error scores in usability tests.

  21. Q20B – is it a correlational study or between-groups design? • Korrelation er en analysemetode. Mange typer eksperimentelle designs kan give ophav til en korrelationsanalyse. • Eksperimentelle design er mere grundlæggende. • I dette tilfælde er der tale om et between-groups (independent measures) eksperiment design – 3 grupper der måles hver for sig • Bemærk: Ikke nødvendigvis et ”true” eksperiment – står ikke noget i opgaven om random allocation af participants

  22. Q21B – skal vi regne SD ud i hånden?? Hvilken SD regner SPSS ud? Den for populationen eller den for samplet? • SD for sample: 8.644507; SD for population: 8.869077 – hvad siger SPSS? • Note: Excel bruger SD for population (N-1)

  23. Q21C – er det +/- 1 SD? (Vel ikke +/- en halv SD?) • +/- 1 SD – når man siger ”within x SD of the mean” betyder det + eller – • Fordi data er normalfordelte ville vi forvente at 68% af de 20 scores lå indenfor en SD i begge retninger

  24. 68% 95% 99.7% Relationship between the normal curve and the standard deviation: All normal curves share this property: the SD cuts off a constant proportion of the distribution of scores:- frequency -3 -2 -1 mean +1 +2 +3 Number of standard deviations either side of mean

  25. The normal distribution • About 68% of scores will fall in the range of the mean plus and minus 1 SD; • 95% in the range of the mean +/- 2 SD's; • 99.7% in the range of the mean +/- 3 SD's.

  26. Q22C – skal 998 tillægges datasættet, nu hvor det ikke kan udelades? • Fejl i opgaven: 998 findes ikke i talrækken. • Ideen var at observere hvordan mean, median, mode og SD ændrer sig forskelligt når scores ændrer sig, dvs. hvorvidt mean, median eller mode er mest ”sårbare”. • Der vil ikke være fejl i eksamenssættet.

  27. Q25 – hvorfor er der 6 values fra hver by, når du skriver at der burde være noget andet? • &%¤&¤ ... Host host ... Nja der burde så stå ”six” i opgaveteksten, ikke ”seven” – det er en fejl. • Hvis det her skulle opstå, så brug ALTID de rå data. Løs opgaven med de data I bliver givet. • Som sagt: Eksamenssættet er grundigt tjekket.

  28. Hvornår bruger vi z-scores?

  29. Going beyond the data: Z-scores Using z-scores, we can represent a given score in terms of how different it is from the mean of the group of scores. SD = 2 μ = 63 Xi = 64 How to calculate z-score: - SD from the mean

  30. Z-scores We can do the same thing to calculate the relationship of a sample mean to the population mean: μ = 63 64 (1) we obtain a particular sample mean; (2) we can represent this in terms of how different it is from the mean of its parent population.

  31. We use z-scores whenever we want to evaluate how far from a sample mean a score is • E.g. to evaluate if a score is an outlier • Hvis f.eks. en score er -1 SD fra mean, så ved vi at den falder indenfor de 68% hyppigste scores (grundet normalfordelingen i dataene) – dvs. ikke statistisk signifikant ved p<0.05 • Or, conversely, how far away from the population mean our sample mean is

  32. Hvordan finder man ud af om scores i et datasæt er normalfordelt?

  33. Parametric statistics • Parametric statistics work on the mean -> All data must be interval or ratio level data • Parametric tests alsomake assumptions about the variance between groups or conditions • So we must BOTH have parametric measure AND scores must adhere to the requirements of parametric statistics

  34. Parametric statistics • For independent-measures (between groups), we assume that variance in one condition is the same as the other: Homogeneity of variance • The spread of scores in each sample should be roughly similar • Tested using Levene´s test (we do this in SPSS – often i gives you Levene´s test when running e.g. T-test) • For repeated-measures (within subjects), we operate with the sphericity assumption, • Tested using Mauchly´s test • Basically the same thing:homogeneity of variance

  35. SPSS output (independent measures t-test) t is calculated by dividing difference in means with standard error: 4.58/0.84359 Sig. is < than .05, so there is a significant difference between alcohol/no alcohol on performance Row 1 left show result of Levene´s test – tests the hypothesis that variance in the two samples is equal. If Levene´s test is significant at p<0.05 the assumption of homogenity of variance in the samples has been violated (this is annoying). If not, we assume equal variance (use row 1)

  36. Parametric statistics • We also assume our data come from a population with a normal distribution • We can test how much a distribution is similar to the normal distribution using the Kolmogorov-Smirnov test (the vodka test) and the Shapiro-Wilk tests • The tests compare the set of scores in the sample to a normally distributed set of scores with the same mean and standard deviation • If the test is non-significant (p>0.05) the distribution of the sample is NOT significantly different from a normal distribution (i.e. it is normal) [OPPOSITE OF LEVENE´S TEST!] • If p<0.05, the distribution of the sample is significantly different from normal (e.g. positively or negatively skewed).

  37. Parametric statistics • We can run Kolmogorov-Smirnov and Shapiro-Wilk tests in SPSS • The most important is the Kolmogorov-Smirnov Test(K-S-test) • SPSS produces an output that includes the test statistic itself (D), the degrees of freedom (df) (= the sample size) and the significance value of the test (sig.). • If the significance of the K-S-test is less than .05, the distribution deviates significantly from the normal

  38. Brush-up on standard deviation from the mean • SD from the mean is just how many SD´s your score/result deviates from the mean value of the sample/population