Statistics lectures and summary book Andy Field Discovering - Statistics (4th edition)
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Course
Statistics
Institution
Tilburg University (UVT)
Lecture notes in right order. Each statistical test (One-sample t-test, Independent t-test, Dependent t-test, One-way ANOVA, Factorial ANOVA, Correlation, Regression, Chi-square) is explained by the use of presentations given by the lecturer and matching chapters of the book. I also made a handbook...
Statistics
Course and exam material
Chapter 1 (whole)
Chapter 2 (whole)
Chapter 3 (whole, except for section 3.7, which is optional but very handy to know)
Chapter 4 (up to section 4.8.3), plus 4.9
Chapter 5 (whole)
Chapter 7 (whole)
Chapter 8 (8.1, 8.2, 8.3, and 8.4)
Chapter 9 (whole)
Chapter 11 (whole)
Chapter 13 (whole)
Chapter 17 (17.9 and 17.10)
Chapter 18 (18.1, 18.2, 18.3, 18.4, 18.5)
Chapter 1
Quantitative methods= Numbers are involved in research.
Qualitative methods= Test theories by analyzing language.
From observations you generate explanations, theories, from which you can make predictions
(hypothesis). What to measure? We need measure variables to test hypothesis. → Two options:
Observing what naturally happens (correlational/cross-sectional research. Longitudinal is measuring
repeatedly at different points of time, this helps to see the congruity between different variables,
which came first. In correlational research there could be a third variable, tertium quid. Correlational is
ecological validity because something is not influenced by the researcher) or manipulate some
variable and observe (experimental research).
Unsystematic variation= Different performances because of unknowing factors.
Systematic variation= Different performances because you manipulated themselves.
A statement can be proved or disproved, otherwise it is not a scientific statement.
The dependent variable depends on the independent variable.
Independent variable= A variable we think it’s a cause. Value does not depend on other variables.
Dependent variable= Variable we think it’s an effect. This depends on the cause.
Randomization= unsystematic variation.
Level of measurement= Kilo/Euro.
Measurement error= You are 83 kg, but the measurement scale says 80 kg. The error is 3 kg.
Validity= whether the instrument actually measures what it sets out to measure.
➔ Criterion validity= Establish that an instrument measures what it claims to measure
through comparison to objective data.
➔ Concurrent validity= When data are recorded at the same time with a new instrument
but the same criteria.
➔ Predictive validity= Data of a new instrument can predict observations at a later point
of time.
➔ Content validity= Cover the full range of the construct.
Reliability= Instrument is consistent across situations. Reliability must be first before validity.
, ➔ Test-retest reliability= Test the same group of people twice.
Frequency distribution= How often a score occurs. Can be positively and negatively skewed. Also can
be negative and positive kurtosis (low and high in the tails).
Negatively skewed Normal distribution Positively skewed
distribution Symmetrical distribution
or Skewed to the left Skewness = 0 or Skewed to the right
Skewness <0 Skewness > 0
Platykurtic distribution Normal distribution Leptokurtic distribution
Thinner tails Mesokurtic distribution Fatter tails
Kurtosis <0 Kurtosis = 0 Kurtosis > 0
Normal distribution= Left and right are the same. This is when everything is very close to each other. A
mean of 0 and a standard deviation of 1.The z-scores are the resulting scores. You choose a value to
see what’s is in that part of the graphic (je trekt een lijn in de grafiek).
z= Value – Mean
Standard deviation
We always look for the center of the distribution (central tendency).
- Mode= score that is most frequently.
- Median= (aantal soorten scores + 1)/2. Simply the middle score when you order the data. If the
score is even, take the average of the two middle. With the median you have to work with the
interquartile range, this is the difference between de half of each half from the median.
- Mean= The average score. But also gives an indication for someone if you know nothing.
➔ Deviance (afwijking) is calculate the difference between each scores and the mean (je
doet letterlijk de mean min de value).
➔ Sum of squared deviations is first calculate the mean, than find the deviance and then
square them (bijv. Als het 20 is wordt het 400 want je doet x, vermenigvuldigen. De –
mag hier weggelaten worden). And you sum them up for every value. Then you could
calculate the…
➔ Variance. Divide the sum of squares in the number of observations (N). Enabling us to
compare variability across samples.
➔ Standard deviation quantifies the amount of variation in a set of data. Small means data
points are close to the mean. Take square root (wortel, because it becomes a measure
that we can interpret again) of the outcome of the variance. Most of the time this is 3.
First sum of squares → Variance (in kwadraat) → Standard deviation (wortel). This
varies across the width of samples.
, Probability= How likely it is that a score would occur. Probability distribution is a curve with x (variable)
and y (probability that it will happen).
Lecture 1
The research process (Early stage of the research process)
Initial observation
Find something that needs explaining
- Observe the real world
- Read other research to see:
Whether someone else has made the same observation you have,
Whether there is a theory that might explain why you observe what you observe
We observe data all the time. If we see it more times, we can say that it is a theory (a set of principles
that informs you how reality works). We could develop a theory (ex. Woman are more likely to wear
dresses in our culture).
Theories and hypothesis
Theories= An hypothesized general principle or set of principles that explain known findings about a
topic and from which new hypotheses can be generated.
Hypothesis= A prediction (scientific statement) from a theory.
From a theory you can develop hypothesis (ex. ‘All woman wear dresses’ has to be rephrased → you
could say ‘woman are more likely than man to wear dresses’. But because we want to disprove we
need to rephrase it in a new statement ‘Men and woman are equally likely wearing a dress or a skirt.
You don’t change the words man and woman but rephrase it. This hypothesis is called H1. You also
have the H0 = Alternative Hypothesis (Null Hypothesis). With the H1 we try to reject the H0.
H1 is de vraag om te bewijzen dat H0 niet klopt.
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