Samenvatting GZW1026 Introductie Statistische Methoden D - € 4.25
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Samenvatting GZW1026 Introductie Statistische Methoden D

Uitgebreide samenvatting van het blok statistiek in het Engels, met name voor iedere seminar de uitleg over de video's en Andy Fields boek.


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GZW1026

Introductie statistische
methoden voor D
Seminars: videos + Andy field

2016-2017

Inhoudsopgave
Seminar 1.1.............................................................................................................................................. 3
Types of variables NOIR .................................................................................................................. 3
Discrete and continuous variables ....................................................................................................... 7
Histograms .......................................................................................................................................... 7
Histograms .......................................................................................................................................... 8
Central tendency: Mean, median, and mode ....................................................................................... 9
Range, Standard deviation/variance .................................................................................................... 9
Interquartile Range (IQR) ................................................................................................................. 10
Normal Distributions, Standard Deviations, Modality, Skewness, Kurtosis ..................................... 10
Normal Distribution .......................................................................................................................... 13
Interpreting boxplots ......................................................................................................................... 15
Andy Field ......................................................................................................................................... 16
Seminar 1.2............................................................................................................................................ 20
Normal distribution: Z-score ............................................................................................................. 20
Correlation ......................................................................................................................................... 21
Simple linear regression .................................................................................................................... 24
Least squares regression line ............................................................................................................. 26
Interpreting parameters...................................................................................................................... 28
Calculating R-square R .................................................................................................................... 30
Andy Field ......................................................................................................................................... 35
Seminar 2.1............................................................................................................................................ 39
Andy Field ......................................................................................................................................... 39
Seminar 2.2............................................................................................................................................ 40
The central limit theorem and the sampling distribution of the sample ............................................ 40
Sampling distribution of mean .......................................................................................................... 41
Understanding Confidence Intervals ................................................................................................. 43
Calculating the Confidence interval for a mean using formula ......................................................... 45
Andy Field ......................................................................................................................................... 47
Seminar 3.1............................................................................................................................................ 48
Hypothesis tests, p-value ................................................................................................................... 48
Understanding the p-value................................................................................................................. 51
Type 1 error = error of rejection ........................................................................................................ 53
Introduction Hypothesis testing......................................................................................................... 54
Z tests for One Mean ......................................................................................................................... 56
T tests for one mean .......................................................................................................................... 60
Type I errors, type II errors, power ................................................................................................... 64


Statistical versus practical significance ............................................................................................. 66
Relationship between confidence intervals and hypothesis tests ...................................................... 67
t tests for one mean: example ............................................................................................................ 69
Andy Field ......................................................................................................................................... 70
Seminar 3.2............................................................................................................................................ 71
Hypothesis tests on one mean: t or z ................................................................................................. 71
Inference for two means: Introduction .............................................................................................. 73
Pooled-Variance t Tests and Confidence Intervals: Introduction ...................................................... 75
Unpooled variance t tests and confidence interval: Introduction ...................................................... 78
An introduction to paired-difference procedures .............................................................................. 81
Andy Field ......................................................................................................................................... 83
Seminar 4............................................................................................................................................... 84
Chi-square Tests of Independence..................................................................................................... 84
Contingency Table Chi-Square Test ................................................................................................. 85
Inference on the slope........................................................................................................................ 86
Simple linear regression. Always plot your data ............................................................................... 88
The pooled-variance t-test as a regression......................................................................................... 89
Simple linear regression: Checking assumptions with residual plots................................................ 90
Andy Field ......................................................................................................................................... 92


Seminar 1.1
Types of variables NOIR
Lowest: nominal ordinal interval ratio :highest

NOIR

NOMINAL
Nom just categories
Classification of data
- Lowest level of measurement
- Discrete categories
o each category
has a criteria that variable has or does not have
- No natural order
o Category has numbers but the numbers dont have a meaning, but they are simple
labels
- Categorical or dichotomous
o Categorical: more than 2 possible values
Group membership: 1 experimental
2 placebo
3 routine
o Dichotomous: 2 values
Example: Gender: 0 female
1 male
Marital status colour, religion, type of car
- May be referred to a qualitative or categorical
o Its not a miracle
Possible measures:
- Mode: only one that makes sense
- Modal percentage
- Range
- Frequency distribution
Calculate a mean,.. is not possible

ORDINAL
Ordinal data can be counted and ordered but not measured (no mean or average)
- Ordered categories/Order matters
o But not the difference between values
o Unknown distance between rankings
- Relative rankings
o Likert scales unknown of each category is equal you dont know the differences
on a scale the value between a 9 and a 10 is necessarily not equal as between a 4
and a 5
o Socioeconomic status 1 low
2 middle
3 high
o Pain intensity
o Non-numeric concepts
o Size: 1 small 2 medium
3 large
o Size, ranking of favorite sports, class rankings, wellness rankings


-


Unknown distance between rankings
o Interval between these numbers is not necessarily equal
Zero is arbitrary no absolutely zero
Attitudes and perceptions

Nominal ordinal: categories have a natural order to them
Possible measures:
- All nominal level tests
- Median
- Percentile
- Semiquartile range
- Rank order coefficients of correlation

INTERVAL
space in between
Orders + values on a scale
- Ordered categories
- Equal distance between values direct measurement quality
o Can measure differences
- An accepted unit of measurement
- Zero is arbitrary 0 is an additional point of measurement
Examples
o Test in school: 0/10 does not mean you have no knowledge
o Temperature: 0C does not mean there is no temperature
o Elevation: level 0 does not mean there is no level
o Time
Possible measures: more tests
- All ordinal tests
- Mean
- Mode
- Standard deviation
- Addition and subtraction cannot multiply or divide
Problem: dont have a true zero: multiply, divide or calculate ratios

RATIO
Precise, ordered and exact
- Most precise
- Ordered
- Exact values
- Equal intervals
- Natural zero
zero is absolute 0=0: absent of measurement
o when the variable equals o it means there is none of that variable
o Not arbitrary

Possible measures: (fysical)
- Weight
- Height
- Pulse
- Blood pressure


-


Time
Degrees Kelvin
All operations are possible
o Descriptive and inferential statistics
Can make comparisons
o An 8 kg baby is twice as heavy as a 4 kg baby
Can add, subtract, multiply, divide (ratios)

Nominal is named
Ordinal is ordered
Interval has a none interval
Ratio has a true zero


Statistics used should be appropriate for the level of data as well as the research question


Discrete and continuous variables
Random variables (RV)
- Discrete RV
- Continuous RV

distinct or separate values list and count the values
can take any value in an interval not list or count the values

Examples:
X= (1 heads 0 tails)
Discrete RV
you can count the number of difference value
Y= the exact mass of a random animal selected at the New Orleans Zoo
Continuous RV
the exact mass: nobody knows the exact numbers of protons, any value in between (f.e.:
123,78738949 kg)
Y= the year that a random student in a class was born
Discrete RV
The year could be 1985 1993 2001
Z= number if ants born tomorrow in the universe
Discrete RV
You can count the values
X= the exact winning time
Continuous RV
The precise time: cant be count (any value between 5 sec and 12 sec: 6,2 6,3 6,23984)
X= winning time for the mens 100 m dash at 2016 Olympics rounded to the nearest 100
Discrete RV
Count and list them

Histograms
The most used way to present/visualize data
1, 4, 2, 1, 0, 2, 1, 0, 1, 2, 1, 0, 0, 2, 2, 3, 1, 1, 3, 6
How frequent are each of these numbers Categorize them in categories


How much have we of each number


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