This summary contains everything you need to know for the course 'Kwantitatieve Onderzoeksmethodologie' (in Dutch) at Radboud.
Note: If you want more chapters of Field's book, I have a bundle containing two summaries, each with different chapters summarised.
Discovering Statistics Using IBM SPSS Statistics
Andy Field
Content
Chapter 2. The Spine of Statistics...........................................................................................................2
Chapter 6. The Beast of Bias...................................................................................................................4
Chapter 9. The Linear Model (Regression).............................................................................................6
Chapter 11. Moderation, Mediation and Multicategory Predictors.....................................................12
Chapter 12. GLM 1: Comparing Several Independent Means...............................................................14
Chapter 13. GLM 2: Comparing Means Adjusted for Other Predictors (Analysis of Covariance)..........14
Chapter 14. GLM 3: Factorial Designs...................................................................................................15
Chapter 17. Multivariate Analysis of Variance (MANOVA)...................................................................16
.............................................................................................................................................................16
Chapter 18. Exploratory Factor Analysis...............................................................................................17
Chapter 19. Categorical Outcomes: Chi-Square and Loglinear Analysis...............................................21
Chapter 20. Categorical Outcomes: Logistic Regression.......................................................................23
1
,Chapter 2. The Spine of Statistics
The SPINE of statistics stands for:
Standard error
Parameters
Interval estimates (confidence intervals)
Null hypothesis significance testing
Estimation
Outcomei = model + errori
Models are: regression, moderation, ANOVA, multilevel model, t-test, mediation, and correlation.
Population can be very general (all human beings) or very narrow (all male ginger cats called Bob).
A sample is a smaller subset of the population from which the data is collected.
Degrees of freedom = number of scores used to compute the total adjusted for the fact that we're
trying to estimate the population value.
The sum of squared errors and the mean squared errors (variance) can be used to assess the fit of a
model.
Method of least squares or ordinary least squares (OLS) = the principle of minimizing the sum of
squared errors.
Sampling variation happens because they contain different members of the population.
Sampling distribution is the frequency distribution of sample means (or any other parameter) from
the same population.
The sampling distribution tells us whether sample means are typically representative of the population
mean.
The standard error of the mean (SE) or standard error is the standard deviation of sample means.
It measures how representative of the population a sample mean is likely to be.
A large standard error (relative to the sample mean) means that there is a lot of variability
between the means of different samples and so the sample mean we have might not be
representative of the population mean.
A small standard error indicates that most sample means are similar to the population mean.
Central limit theorem = when the sample is sufficiently large (n > 30), the sampling distribution will
be (approximately) a normal distribution.
The confidence interval for the mean is a range of scores constructed such that the population mean
will fall within this range in 95% of samples.
It is NOT an interval within which we are 95% confident that the population mean will fall.
Example: a confidence interval of 95% means, 95% of your samples will contain the population value.
The point estimate is a single value from the sample.
An interval estimate is when we use our sample value as the midpoint but set a lower and upper limit
as well.
Lower boundary of confidence interval = mean - (z-score interval * standard error)
Upper boundary of confidence interval = mean + (z-score interval * standard error)
Small samples have a t-distribution.
t-distribution = a family of probability distributions that change shape as the sample size gets bigger.
2
, Null hypothesis significance testing (NHST) is a method for assessing scientific theories. The basic
idea is that we have two competing hypotheses:
1. Alternative hypothesis: an effect exists (also called experimental hypothesis).
Example: if you imagine eating chocolate you will eat less of it.
2. Null hypothesis: an effect doesn't exist.
Example: if you imagine eating chocolate you will eat the same amount as normal.
We compute a test statistic that represents the alternative hypothesis and calculate the probability that
we would get a value as big as the one we have if the null hypothesis were true. When the probability
(p-value) is:
< 0.05 we reject the idea that there is no effect and say that we have a statistically
significant finding.
> 0.05 we do not reject the idea that there is no effect, and we say that we have a non-
significant finding.
Hypotheses can be directional or non-directional:
Directional: an effect will occur + the direction in which it will occur. Example: more or less.
Non-directional: an effect will occur, but no direction is mentioned.
A test statistic is a statistic for which we know how frequently different values occur.
signal variance explained by t h e model effect
Test statistic= = =
noice variance not explained by t h e model error
signal ¿ parameter effect
Test statistic= = =
noice sampling variation∈t h e parameter error
One-tailed test: a statistical model that tests a directional hypothesis.
Two-tailed test: a statistical model that tests a non-directional hypothesis.
If your one-tailed test results go the opposite way you expected, ignore them, and go with the null
hypothesis. Doing otherwise means using a different significance level in a two-tailed test.
There are two types of errors one can make when testing hypotheses:
Type I error occurs when we believe that there is a genuine effect in our population, when in
fact there isn't.
α = probability of making a Type I error.
Type II error occurs when we believe that there is no effect on the population when, in reality,
there is.
β = probability of making a Type II error.
Familywise or experiment-wise error rate = the probability of making a Type I error in any family
of tests when the null hypothesis is true in each case. The 'family of tests' can be loosely defined as a
set of tests conducted on the same data set and addressing the same empirical question.
Statistical power = the ability of a test to find an effect = 1 - β
It depends on:
How big the effect is.
How strict we are about deciding that an effect is significant.
The sample size.
3
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