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.

Rules for the use of PCs at exams:http://www1.itu.dk/sw118342.asp#5

16_92142

Rules for DEDA exam specially:http://www1.itu.dk/graphics/ITU-libra

ry/Intranet/Uddannelse/Eksamen/PC-regler/Regler%20for%20brug%20af%20PC%20ved%20eksamen%20i%20Experimental%20Design%20and%20Analysis.pdf

Multiple choice sektionen:

Der kan være flere svarmuligheder til spørgsmålene.

Der kan være flere svarmuligheder på 0+ af spørgsmålene

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

Using SPSS to obtain scatterplot with regression line:Analyze > Regression > Curve Estimation...

Model Summary and Parameter Estimates

Dependent Variable: memory score

.736 16.741 1 6 .006 17.167 8.333EquationLinear

R Square F df1 df2 Sig.

Model Summary

Constant b1

Parameter Estimates

The independent variable is number of vitamin treatments.

”constant" is the intercept with y-axis, "b1" is the slope”

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

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

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 the deviations of the predicted X's from actual X's - a different task (although somewhat similar)!

Solution: To calculate regression of X on Y, swap the column labels (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

Regression lines for predicting Y from X, and vice versa:

stress score (X)

test score (Y)

0

20

40

60

80

100

120

0 10 20 30 40 50

X on Y: predicts test score, given knowledge of stress score

n.b.: intercept = 55

Y on X: predicts stress score, given knowledge of test score

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.

Values are measureableMeasuring size of variables is important

for comparing results between studies/projects

Different measures provide different quality of data:

Nominal (categorical) dataOrdinal data Interval dataRatio data

Non-parametric

Parametric

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

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

Ordinal data

Provides information about the ordering of the data

Does not tell us about the relative differences between values

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

Interval data

When measurements are made on a scale with equal intervals between points on the scale, but the scale has no true zero point.

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!

-4 -3 -2 -1 0 1 2 3 4

1 2 3 4 5 6 7 8 9

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.

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

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)

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

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:-

-3 -2 -1 mean +1 +2 +3

Number of standard deviations either side of mean

fre

qu

enc

y

99.7%

68%

95%

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.

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.

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.

Hvornår bruger vi 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.

Xi = 64μ = 63

How to calculate z-score:

50.02

1

2

6364

i

X

Xz

Going beyond the data: Z-scores

SD = 2

- SD from the mean

We can do the same thing to calculate the relationship of a sample mean to the population mean:

(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.

μ = 63

zX

X N

64 63

2

16

12

4

2.00

64

X

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

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

Parametric statistics work on the mean -> All data must be interval or ratio level data

Parametric tests also make 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

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

SPSS output (independent measures t-test)

t is calculated by dividing difference in means with standard error: 4.58/0.84359

Row 1 left show result of Levene´s test – tests the hypothesis that variance in the twosamples 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)

Sig. is < than .05, so there is a significant difference between alcohol/no alcohol on performance

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).

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

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