Summary SMCR Notes by Laura Oller Prados (55 pages) that got me a 9.7!
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Course
SMCR
Institution
Universiteit Van Amsterdam (UvA)
This book summary includes all theoretical content from the SMCR book in a much-needed comprehensive way, and it got me a 9.7 in the course. I encourage you to also practice with the interactive SPSS videos in the book.
Everything is reported with 2 decimals, but the p value with 3.
Personal notes / Additional explanations in green.
Examples in blue.
By Laura Oller Prados.
SMCR NOTES
Do frequencies at the beginning to check data for missing values.
Include at least 1 comment per command in the SPSS syntax. No errors. Do not paste
PROCESS, just write something like “* Use PROCESS Model 6, with efficacy as Y,
compare as first mediator (M), bodydiss as second mediator (M), and exposure as X.”.
/ 2022
LECTURE – INTRODUCTION:
Inferential statistics are those that study a sample to try to make a statement about a population.
- If p < .05 the test is statistically significant, so we reject the null hypothesis.
p value = The probability of drawing a sample that is at least as different from the null
hypothesis than our sample, if the null hypothesis is true.
If we have a representative sample, we can say something about the population without the
need of drawing many different random samples and calculating their average.
We can never know if a dice (research instrument) is biased or not, but after a sufficient number
of attempts, we can be confident (we create a confidence interval).
Moderation = Different effects for different groups, so the regression lines representing them
are different and have their own unique regression equations (accounting for different slopes).
Conditional effects.
Mediation = A third variable that explains the relationship between two variables. Indirect
effects and causality.
1
, Everything is reported with 2 decimals, but the p value with 3.
Personal notes / Additional explanations in green.
Examples in blue.
By Laura Oller Prados.
Bivariate = 2 variables.
Multivariate = 3 or more variables.
/ 2022
CHAPTER & SESSION – 1:
Regression coefficients are formulae that can predict the effect of x on y based on results from
our sample.
Statistics is a tool used to check the accuracy of statements about the observable world
(population) via data collected from it (sample(s)). The objective is to arrive to general
statements true to many situations. Since data collection is costly, we strive for making the
most of as little (representative) data as possible. Inferential statistics allow this, generalizing
from a smaller set of random observations.
Two random samples from the same population CANNOT or CAN be identical.
A sample is representative if its variables are distributed in the same way as in the population,
which we know can happen or not due to chance, that is why a random sample is in principle–
and not strictly–representative of the population.
Inferential statistics allows to generalize sample conclusions to a wider population by offering
us a p value and a confidence interval.
Statistical inference is about estimation and null hypothesis testing, central element being
sampling distributions. We collected data on a random sample and we want to draw conclusions
(make inferences) about the population from which the sample was drawn. From the proportion
of yellow candies in our sample bag, we want to estimate a plausible range of values for the
proportion of yellow candies in a factory’s stock (confidence interval). Alternatively, we may
want to test the null hypothesis that one fifth of the candies in a factory’s stock is yellow.
Sampling distribution = The crucial link between the population and the random sample
(drawn from it) which allows us to make generalizations about mentioned population.
It’s basically a distribution of thousands of random samples; only one sample would not be
enough evidence to draw the correct proportions in the population since it might be randomly
different from the rest. Different from the sample distribution, the chart of a single sample.
- A distinction: In a sampling distribution, we observe samples (units of analysis, i.e.,
bags of candies) and measure a sample characteristic/statistic (i.e., yellow colored) as
the random variable. Differently, in the population and in the sample, we use candies
as units of analysis instead of sample bags.
2
, Everything is reported with 2 decimals, but the p value with 3.
Personal notes / Additional explanations in green.
Examples in blue.
By Laura Oller Prados.
Sample statistic = The variable being observed, yellow candies, which is depicted in the x-
axis aka the sampling space (while the probabilities are depicted on the y-axis).
Sample result = The number of yellow candies.
Dividing the number of samples with a certain characteristic by the total number of samples
drawn (total in the sampling distribution), we get the probability of drawing the certain
characteristic sample. For example, if 26 out of all 1000 samples have five yellow candies, the
proportion of samples with five yellow candies is = 0.026. Then, the probability of
drawing a sample with five yellow candies is 0.026 (we usually write: .026).
Probabilities can be expressed both as a proportion or as a percentage.
Expected value / Expectation / Mean of sampling distribution = Population value /
parameter.
In other words, calculating the mean of the sampling distribution gives the true population
value, as long as the sample statistic is unbiased. It represents the “balance point” of a
distribution.
For example, if the proportion of yellow candies in the population is known to be 20%, in a
bag of 10 (0.20 × 10) there’ll be 2, and in a bag of 5 (0.20 × 5) there’ll be 1.
A sample statistic is called an unbiased estimator of the population statistic / parameter if the
expected value (mean of the sampling distribution) is equal to the population statistic. If the
sample statistic’s value neither systematically overestimates or underestimates the population
value.
- Downward biased estimate = An underestimation of the parameter; we say that
there must be 2 candies in the population because we have 2 candies in our sample, the
estimate is too low. This is why we don’t generalize the number of candies but the
proportion.
3
, Everything is reported with 2 decimals, but the p value with 3.
Personal notes / Additional explanations in green.
Examples in blue.
By Laura Oller Prados.
- Sometimes, adjustments are needed, but our software does it for us. It’s the case of
the sample’s standard deviation and variance, which must be calculated in a special way
to obtain an unbiased estimate of the population’s SD and variance.
Probability distribution = A sampling space on the y-axis with a probability (between 0 and
1) for each outcome of the sample statistic. The sampling distribution is an example of a
probability distribution simply because it includes/represents probabilities in the y-axis.
Probabilities always sum to 1.
1. Discrete distributions list the probability of each outcome separately because there’s
a limited number of outcomes possible, i.e., 0 to 10 candies. It’s a bar chart.
2. Continuous distributions, i.e., weight, where we can discern endless intermediate
values, we are interested in the averages. However, the possibility of finding whichever
average weight will always be virtually 0 because there’s an infinite number of possible
outcomes. For example, we want to know the probability of 2.8 grams, but then we are
excluding 2.81, 2.801… and it is very unlikely to draw an average weight of 2.8 grams
exact. The probability of drawing continuous sample statistic’s characteristics is always
virtually 0, so we must use probability density.
In probability density, we look at a range of values instead of a single value, using at
least 2.8 grams, at most 2.8 grams, or between 2.75 and 2.85 grams. It is represented as
an area between the x-axis and a curve. It’s the normal distribution/curve.
Left-hand probability = The probability of drawing values up to (and including).
Right-hand probability = The probability of drawing values above (and including).
By being interested in a sample mean, like the average candy weight, we have means
at 3 levels (the mean of the sampling distribution is a mean of means):
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