This document contains all the notes of the lectures of statistics 3. The notes are mostly in English but are completed in Dutch. There are college slides for examples and SPSS output. Everything that was discussed during the lectures is in this document
notes lectures statistics 3 clinical lesson ilja chris psychology bachelor year 3 2019 2020 period 4
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Statistiek 3
College 1
Beschrijvende statistieken
- “Statistics is the science of collecting, organizing and interpreting numerical facts, which we call
data.”
- A&F: Statistics consists of a body of methods for obtaining and analyzing data, to:
1. Design [research studies that]
2. Describe [the data to]
3. Make inferences based on these data.
- Descriptive Statistics:
- Descriptive statistics summarize sample or population data with numbers, tables, and
graphs
- Inferential Statistics:
- Inferential statistics make predictions about population parameters, based on a (random)
sample of data.
Data, population, sample, reliability and validity
- Doing research using data:
- Population: the total set of participants, relevant for the research question
- E.g. Population parameter: average hour of self study per week of all students.
- Sample: a subset of the population about who the data is collected
- E.g. Sample statistic: average hour of self study per week of a randomly selected
sample of 800 students
- Good quality data is necessary to answer the research question:
- Reliability (Precision)
- Validity (Bias)
Beschrijvende statistieken
- Variable: measures characteristics that can differ between subjects
- Types: behavior-, stimulus-, subject-, physiological variables
- Measuring scales (NOIR):
- Categorical/qualitative
- Nominal unordered categories (Eye color, Gender)
- Ordinal ordered categories (Disagree/Neutral/Agree)
- Quantitative/numerical
- Interval: equal distance between consecutive values (°C)
- Ratio: equal distance and true zero point (K)
1
,- Range:
- Discrete: measurement unit that is indivisible (# Brothers/sisters)
- Continuous: infinitely dividable measurement unit (Body Length)
- Three dimensions are of importance:
- Central tendency
Gives information about the typical observation: mean, mode, median …
- Dispersion
Gives information about the extent to which a distribution is stretched or squeezed:
standard deviation, variance, interquartile range
- Relative position measures
- Gives information about relative positions of observations: percentile, quartile, …
Beschrijf deze twee verdelingen:
- de centrale gevoeligheid is vrijwel hetzelfde
- vb. zelfde gemiddelde
- het lijken normale verdelingen -> geen scheefheid
- de variantie van B is lager en daardoor is hij preciezer
Inferentiële statistiek
- Goal: reliable and valid statements about the population based on a sample
- Sample statistic should not differ from population parameters
- Problems:
- Sampling error - “Random sample differences”
- Sampling bias - “Bias due to selective sample”
- Response bias - “Bias due to incorrect answer”
- Non-Response bias - “Bias due to non-response (missings)”
- Solution:
- “A random (or other probability) sampling approach of sufficient size that generates data
for everyone approached, with correct responses on all items for all subjects.”
- door vaker te testen voorkom je persoonlijke fouten door omstandigheden
- 3 verdelingen:
- Population distribution
- Student proportions indicating to be (not) in need for extra math support
- Sample data distribution
- Student proportion of the sample (here n = 1000) indicating to be (not) in need for
extra math support
- Sampling distribution
2
, - The probability distribution for the sample statistic. To interpret as the result of
repetitive taking of a sample of size n (here 1000).
π (1−π ) 0.38(1−0.38)
- Standard deviation of:
√ n √
=
1000
- Standard error (σM) estimated by SEM
= 0.015
- Central Limit Theorem for sampling distribution
- Empirical rule for normal distribution
- 68% within ± 1σ of the mean
- 95% within ± 2σ of the mean
- almost 100% within ± 3σ of the mean
- als je een sample van ongeveer 30 hebt, krijg je “altijd”
een normaal verdeling onafhankelijk van de populatie-
verdeling
- Relationship between population-, sample- and sampling- distribution
Types van verdelingen
- (Standard-) normal distribution (Z-distribution)
- Sampling distribution of a proportion if H0 applies.
- (Sampling distribution of a mean if H0 applies and if the population standarddeviation is
known)
- Student’s t-distribution
- Sampling distribution of a mean if H0 applies and if the population standard
deviation is unknown.
- Sampling distribution of a regression coefficient if H0 applies.
- Chi-square distribution
- Sampling distribution for deviations of frequencies of a categorical variable if H0
applies.
Scheefheid van verdelingen
Hypothesis Testing
- Significance-test or hypothesis-test:
- Based on a sample, this test determines how strong the evidence is against a certain
3
, hypothesis, upon which a decision is made (not) to reject this hypothesis.
- 5 steps of a hypothesis test:
- Formulate expectations
- Setup hypothesis
- Calculate test-statistic (e.g. t-value)
- Determine p-value
- Draw conclusion
Type 1 en II fout
- Probability of a Type I-error (false positive) is determined by:
- The chosen significance level (α).
- Probability of a Type 2-error (false negative) is determined by:
- Effect size
- Sample size
- Variance (dispersion) in sample
- The smaller the chosen Type I-error, the larger the acquired Type 2-error, given a certain sample.
- je maakt de type 1 en II fout tegelijk
4
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