Exam (elaborations)
Practice questions (+answers) Statistics (GEO2-2217)
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These are practice questions and answers that were presented at the end of each lecture to prepare for the exam.
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Lecture 2:- What types of graphs allow you to represent a distribution of scores, given a
certain situation?
A distribution of scores can be represented by a boxplot, histogram, dotplot, polygons and a bar
chart.
- What metrics do you know to estimate the center of a set of observations?
To estimate the centre of a set of observations you can use the cumulative distribution and the
difference between centres relative to distribution variables. Also the interquartile range can be
used for this purpose.
- What metrics do you know to measure dispersion of your data?
To measure dispersion of data you can use the variance and the standard deviation.
- What metrics do you know to measure differences and how do these allow you to
say something about the size of the difference?
To measure differences you can use the effect size D which indicates whether the difference
between 2 groups is small, medium or large. The larger this effect size is, the larger or stronger
the difference will be.
- In case there are multiple metrics, which one do you use in a given situation, based
on what criteria?
When there are multiple metrics involved, you can use what they ask you to. When there are
quartiles given or when you get information on the mean and the number of observations you
can use either variance or standard deviation. When they specifically ask for an effect of the
difference, you use the effect size D.
Lecture 3:
- Define and explain eta2.
Eta2 = the relative redunction in the sum of squares = (SSd-SSe)/SSd. This metric stands for the
proportion of variation in Y explained by X.
- What is the relation between eta2, D, and r2?
The relation between eta2, D and r2 is that they are all measures for the effect of a difference
between two variables. Eta2 and r2 are hereby both explaining the proportion of variation in Y
explained by X, only with r2 this is the proportion that is linearly explained.
- What is the measurement scale for Y for each one of these metrics?
The measurement scale for Y is as follows: eta2 = (SSd-SSe)/SSd = D2/(4+D2) → r2 = SSl/SSd →
effect size D = difference between means/standard dev.
- What is the summation rule for variation, and how and when does it apply?
The summation rule for variation is SSd = SSg + SSe, when we talk about a mean regression and
SSd = SSl + SSe, when we talk about a linear regression.
- Think of a simple example and calculate eta2 and r2. Try to explain to a class mate
how it’s done.
Group 1: 2,4 → group 2: 3,5 → group 3: 4,6 → group means: 3, 4, 5 → overall mean: 4.
- Eta2: SSd = 22 + 02 + 12 + 12 + 02 + 22 = 10 → SSe = 12 + 12 + 12 + 12 + 12 + 12 = 6 → SSg = (12x2) + 02
+ (12x2) = 4 → eta2 = (4/10) = 0,4 → large effect.
Lecture 4:
- What does the standard error of the mean (SE(M)) represent?
The standard error of the mean represents the standard deviation. When there is a large
standard error of the mean this means you have a small sample. The larger the sample the
smaller the standard error of the mean will be.
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