Complete summary Statistics Premaster CIS + Roadmap all tests
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Statistics (800547B6)
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Tilburg University (UVT)
- Summary of all Statistics Lectures (Chapter 1 till 15 of the book learning statistics with jamovi- Danielle J. Navarro & David R. Foxcroft).
- Summary of all Practice Units
- Summary/Roadmap of all tests (!) and all the other important things you need to keep in mind.
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FULL SUMMARY STATISTICS FOR PM – COMMUNICATION AND
INFORMATION SCIENCES
LECTURE NOTES ...................................................................................................................................... 3
LECTURE 1. Variables (CH 1, 2, 3 and notes) ........................................................................................... 3
LECTURE 2. Distribution, Mean, Standard Deviation, Graphs (CH 4 & 5 and notes) ............................ 10
LECTURE 3. Confidence interval (CH 6, (7), 8 and notes) ...................................................................... 23
LECTURE 4. P-value, Type 1 and 2 errors (CH 9 and notes) .................................................................. 32
LECTURE 5. T-Tests, degrees of freedom and effect size (CH 11 and notes) ........................................ 40
LECTURE 6. ANOVA, Omnibus, Planned contrast, Sums of square, Reliability (CH 13, 15.5 and notes)
.............................................................................................................................................................. 53
LECTURE 7. Factorial ANOVA (notes CH 14) ......................................................................................... 73
LECTURE 8. Factorial ANOVA (notes CH 14) ......................................................................................... 86
LECTURE 9. Chi-Square test (notes CH 10)............................................................................................ 91
LECTURE 10. Correlation (notes CH 12) .............................................................................................. 104
LECTURE 11. Regression...................................................................................................................... 116
LECTURE 12. Regression...................................................................................................................... 127
LECTURE 13. Recap ............................................................................................................................. 137
SUMMARY PRACTICE UNITES THEORY ...................................................................................... 149
Practice Unit 1. Introduction............................................................................................................... 149
Practice Unit 2. Distributions .............................................................................................................. 150
Practice Unit 3. Recoding, Computing and Filtering variables ............................................................ 152
Practice Unit 4. Graphs and testing assumptions ............................................................................... 156
Practice Unit 5. T-tests and effect size................................................................................................ 160
Practice Unit 6. ANOVA and follow-up tests ....................................................................................... 169
Practice Unit 7 & 8. Factorial ANOVA ................................................................................................. 184
Practice Unit 9. Chi-Square Test ......................................................................................................... 197
Practice Unit 10. Correlation Coefficient ............................................................................................ 206
Practice Unit 11. Simple linear regression .......................................................................................... 214
OVERVIEW TESTS ..................................................................................................................... 222
RULES .................................................................................................................................................. 224
DATA PREPARATION ........................................................................................................................... 226
ROADMAPS TESTS ............................................................................................................................... 230
One-sample T-test........................................................................................................................... 230
Independent T-test ......................................................................................................................... 231
Paired-sample T-test ....................................................................................................................... 233
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,(One-way) ANOVA........................................................................................................................... 234
Factorial ANOVA ............................................................................................................................. 238
Chi-Square test of association ........................................................................................................ 241
Chi-square goodness-of-fit.............................................................................................................. 243
Correlation analysis......................................................................................................................... 244
Regression ....................................................................................................................................... 247
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,LECTURE NOTES
LECTURE 1. Variables (CH 1, 2, 3 and notes)
Statistics; trying to predict the future. Not just using ‘common sense’ or gut instincts to come up
with an answer. We find it hard to be neutral, to evaluate evidence impartially and without using
pre-existing biases. Statistics helps us to keep our personal biases under control, and it helps us to
stay honest.
The principle of hypothesis testing: have a good sample size. N=10 is less good than a N=10.000. You
need a reprehensive example of the population.
Women are more intelligent than men. --> wrong.
There is a difference in intelligence (IQ) between woman and men. --> better.
Point of departure = assumption that there is no difference. This gives a point of comparison.
If I measure IQ in 1000 persons, and the mean difference between men and women is larger than 5
IQ-points, then it is very unlikely that this difference is ‘coincidence'.
Null hypothesis, H0: This is the one you test with your data. Most of the time, there is no effect. This
is the hypothesis we try to reject.
• Women are equally likely as men to wear a skirt or a dress.
• There is no relationship between age and the number of wrinkles you have.
If there is no difference; you can't reject or accept the hypothesis.
If there is a difference; you can reject the null hypothesis. This one doesn't work; this one doesn't
explain the data. In this way your alternative data is more likely to explain your data.
It is unlikely that someone with a shoe size of 46 comes in the room. So, the H0 can be rejected.
Because it is very unlikely that the data of the 0 hypothesis is correct.
If it is very unlikely that the null hypothesis is true (chances are smaller than 5%), we may conclude
that there is support for our alternative hypothesis.
The alternative hypothesis, H1: If we can reject H0, this one is supported by the data, but not
proven.
• Women are more likely to wear a skirt or dress than man.
• There is a positive relationship between age and the number of wrinkles you have; the older
people are, the more wrinkles they have.
If your H0 is rejected, it supports the H1. You have found support for your H1 but is does not mean
the H1 is true.
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,Experimental designs.
An experiment: you manipulate something, which is supposed to have an effect. Cause --> Effect.
Change only one thing and see the differences. Everything else is kept constant or balanced to
ensure that they have no effect on the results. Randomization: to minimize (but not eliminate) the
possibility that there are any systematic differences between groups, we randomly assign people to
different groups, and give each group a different treatment.
When you wear glasses on your resume, it is more likely to hire someone sooner.
The one thing that has changed are the glasses.
• Cause: the independent variable; the manipulated variable. The glasses.
• Effect: the dependent variable; the effect which is measured instead of manipulated. More
likely to hire someone.
You need to be able to manipulate the variable, for example the glasses. It is not possible to
manipulate wrinkles (to measure this you need a correlational design).
Correlational designs.
A correlational design (non-experimental research); you measure (perceived) reality. You don’t
have as much control as in an experiment because it is a situation in which you can’t or shouldn’t try
to obtain the control (unethical). For example, getting more wrinkles when growing older. This is a
correlational design because you can't follow people all their life to check this.
We don't speak about independent and dependent variables with correlational designs because it is
not possible to manipulate the variables. Instead of that, we speak about:
• Predictor variable; the cause. Smoking effects the health of people.
• Outcome variable; the effect. Smoking isn't the cause of death in general.
Correlation: smoking effects the health of people, but it is not the cause of death.
Experiment Correlational design
Independent variable The proposed cause, which is A predictor variable
manipulated
Dependent variable The proposed effect An outcome variable
Independent variable
- If experiment (experimental design): the proposed cause, which is manipulated
- If survey (correlational design): a predictor variable
Dependent variable
- If experiment (experimental design): the proposed effect
- If survey (correlational design): an outcome variable
- Measured, not manipulated
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,Quasi-experimental design: There are clearly defined 'conditions' but no experimental
manipulations; there is no 'random allocation (toewijzing) of participants to conditions'. For
example, type of bachelor study.
You need to know what the dependent variable and independent variable are. But those variables
can have different values. The variables have measurement levels.
Categorical variables (discrete variables): things that are divided into distinct categories. For
example, gender.
• Binary or dichotomous variable: only two categories. For example, dead or alive.
• Nominal variable: more than two categories. For example, someone is vegetarian, vegan,
fruitarian, etc.
o Binary and nominal variables only allow you to say whether something equals
something or not (equality).
• Ordinal variable: a nominal variable but the categories have a logical order. For example,
whether people got a fail, a pass, a merit or pass Caum Laude.
o Ordinal variables allow you to say something about whether something equals
something or not (equality), but also about the order of things (order).
Continuous variables: things that get a distinct (verschillende) score. For example, age.
• Interval variable: a variable for which the numerical value is meaningful. The difference
between the numbers is interpretable, but the variable doesn't have a ‘natural’ zero value.
Equal intervals on the variable represent equal differences in the property being measured.
When you have a difference in your scale, this difference is the same anywhere else where
you measure. For example, 10-20 cm, 50-60 cm. Or for example, yesterday it was 15 C and
yesterday 18 C, then the 3 C difference between the two is meaningful. Moreover, that 3 C
difference is exactly the same as the 3 C difference between 7 C and 10 C. Notice that the 0
C does not mean: ‘no temperature at all', but the temperature at which water freezes.
Therefore, it is pointless to try to multiply and divide temperatures. It is wrong to say that 20
C is twice as hot as 10 C, and it is weird to try to claim that 20 C is negative two times as hot
as –10 C.
o Interval variables not only allow you to say something about equility and order, but
also about the distance between units (distance).
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, • Ratio variable: the same as an interval variable, but the ratios of scores on the scale must
also make sense. And in this variable zero really means zero, which makes it possible to
multiply and divide. For example, the number of calories in different juices, 40 kcal is twice
as much as 20 kcal. And the response time to record the amount of time somebody takes to
solve a problem is also a ratio variable. For example, Alan takes 2.3 seconds to respond to a
question, whereas Ben takes 3.1 seconds. As with an interval scale variable, addition and
subtraction are both meaningful here. Ben did take 3.1-2.3= 0.8 seconds longer than Alan
did, and Ben took 3.1/2.3=1.35 times as long as Alan did to answer the question
(multiplication and division make also sense here).
o Ratio variables not only allow you to say something about equility, order and
distance, but also about the ratio between measurements (ratio).
There is always a continuous variable to a categorical variable. For example, ages. Someone from the
age of 40 is a continuous variable, but millennials are a categorical variable.
Hyperactivity is positively related to eating sugar --> Both continuous variables.
The more coffee you drink in the 3 hours, the less sleep you have --> coffee = categorical variable,
hours of sleep = continuous
Military rank --> ordinal variable
The Likert scale: a psychological measurement tool in which a scale is used, and the options strongly
disagree - … - strongly agree are presented. We ought to treat Likert scales as ordinal variables, but
it also a lot of researchers use it as interval scale. We usually think of it as being quasi-interval scale
(a rating scale that classifies responses by using ordered options but that lacks equal distances
between all scale points).
To see if the measurements are good, we look at the reliability and validity of a measure.
Reliability: how precisely you are measuring something; the repeatability or consistency of your
measurement. For example, measuring weight by means of a ‘bathroom scale’ (weegschaal). If you
step on and off the scale over and over again, it’ll keep giving you the same answer.
Notice: reliability is different than correctness; if you hold a sack of potatoes on the bathroom scale
it doesn’t match up with your weight, but it still gives you the same answer over and over again.
- Test-retest reliability: consistency over time; if we repeat the measurement at a later date,
do we get the same answer?
- Inter-rater reliability: consistency across people; if someone else repeats the measurement,
will they produce the same answer?
- Parallel form's reliability: consistency across theoretically equivalent measurements; if I use
a different set of bathroom scales to measure my weight, does it give the same answer?
- Internal consistency reliability: if a measurement is constructed from lots of different parts
that perform similar functions (for example a personality questionnaire result is added up
across several questions) do the individual parts tend to give similar answers?
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