Probability refers to the proportion of occurrence when a particular experiment is repeated infinitely often under different circumstances. It is a long-term relative frequency, does not apply to unique events and is dependent on the reference category. Subjective probability refers to the subjective degree of conviction in a hypothesis. Objective probability refers to the long-term relative frequency and is the same probability used in classical statistics. The p-value is the probability of finding a test statistic at least as extreme as the one observed, given that the null hypothesis is true. An X% confidence interval for a parameter is an interval that in repeated use has an X% chance to capture the true value of the parameter. The p-values are only concerned about the null hypothesis, although it is not possible to make statements about the probability of a hypothesis in classical statistics.If the null hypothesis is true, then the p-values drift randomly. Therefore, it is possible that the p-value is significant by chance. This is why stopping rules are imperative in classical statistics. In Bayesian statistics, the Bayes factor does not drift randomly but drifts towards the correct decision.In classical statistics, the stopping rules (1), the timing of explanations (posthoc test or not) (2) and multiple tests influence the conclusion. This is not the case in Bayesian statistics.Classical statistics does not allow for probabilities to be assigned to hypotheses or parameters, whereas Bayesian statistics does allow this.Bayesian statistics is a method of learning from prediction errors. It assumes that probability does not exist but only uncertainty, which has to be quantified in a principled manner. Therefore, in Bayesian statistics, probability can be assigned to a single hypothesis.The data drive an update from prior knowledge to posterior knowledge. This method investigates whereas classical statistics investigates . The Bayes...
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This page bundles the study guides and additional learning materials for the 'Research Methods & Statistics' course at the University of Amsterdam as wirtten by JesperN, the material might be a little outdated for you. Therefore, please check the difference in edition to ensure there are no unforced errors in your own work.
Booksummary with Research methods in psychology by Morling - 3rd edition
Summaries, Exam Questions and Lecture Notes - UvA B1 Psychology - Study Bundle
In this bundle summaries, exam questions and lecture notes will be shared for the study Psychology, Bachelor 1, University of Amsterdam.
For more summaries and other study assistance as provided by JoHo, please check the Startup page Psychology: UvA Amsterdam - Summaries and study services
Summary of Research Methods in Psychology, Morling, 3rd editionPsychology is based on research and studies by psychologists. Psychologists can be seen as scientists and therefore also as empiricists. Empiricists base their conclusions on systematic observations. Psychologists base their ideas about behavior on studies they have carried out with animals on people in their natural environment or in an environment that has been specially made for the research. Anyone who wants to think as a psychologist must think like a researcher.
Who are the producers and consumers in research?
Psychology students who are interested in conducting research, conducting questionnaires, examining animals, the brain or other themes from psychology are called producers of research information. These students will probably publish articles and work as a research scientist or professor. Of course there are psychology students who do not want to work in a laboratory, but who like to read about research with animals and people. These students are seen as consumers of research. They read about research and they can apply what they have read in the professional field, their hobby or friends and family. These students can become therapists, study advisers or teachers. In practice, it is often the case that psychologists take on both roles. They are both producers and consumers of research.
For the subjects that you will still receive during your psychology studies, it is important to know how you can be a researcher. Even if you do not plan to start a PhD after your studies. Of course you have to write a thesis for graduation and your thesis will have to meet the APA standards. The APA
.....read more Statistical Methods for the Social Sciences van Agresti, 5e druk
Deze bundel bevat (zowel Nederlandstalig als Engelstalig) een boeksamenvatting, BulletPoints en TentamenTickets te gebruiken bij de 5e druk van Agresti Statistical Methods for the Social Sciences.
Research Methods & Statistics – Bayesian statistics summary (UNIVERSITY OF AMSTERDAM)
Probability refers to the proportion of occurrence when a particular experiment is repeated infinitely often under different circumstances. It is a long-term relative frequency, does not apply to unique events and is dependent on the reference category.
Subjective probability refers to the subjective degree of conviction in a hypothesis. Objective probability refers to the long-term relative frequency and is the same probability used in classical statistics.
The p-value is the probability of finding a test statistic at least as extreme as the one observed, given that the null hypothesis is true. An X% confidence interval for a parameter is an interval that in repeated use has an X% chance to capture the true value of the parameter. The p-values are only concerned about the null hypothesis, although it is not possible to make statements about the probability of a hypothesis in classical statistics.
If the null hypothesis is true, then the p-values drift randomly. Therefore, it is possible that the p-value is significant by chance. This is why stopping rules are imperative in classical statistics. In Bayesian statistics, the Bayes factor does not drift randomly but drifts towards the correct decision.
In classical statistics, the stopping rules (1), the timing of explanations (posthoc test or not) (2) and multiple tests influence the conclusion. This is not the case in Bayesian statistics.
Classical statistics does not allow for probabilities to be assigned to hypotheses or parameters, whereas Bayesian statistics does allow this.
Bayesian statistics is a method of learning from prediction errors. It assumes that probability does not exist but only uncertainty, which has to be quantified in a principled manner. Therefore, in Bayesian statistics, probability can be assigned to a single hypothesis.
The data drive an update from prior knowledge to posterior knowledge. This method investigates
whereas classical statistics investigates 
.
The Bayes factor can also be seen as the predictive updating factor for the posterior belief. It is the ratio of likelihoods. The likelihood refers to the probability of obtaining the data given the hypothesis. Bayesian statistics use Bayes rule:
The prior distribution determines the posterior distribution, therefore, a high predictive updating factor in favour of the alternative hypothesis does not necessarily mean that the alternative hypothesis is better. It only predicts the dataset X times better than the null hypothesis in this case.
The posterior belief and the Bayes factor are the same if the prior belief is that the distribution is 50/50. Otherwise, the posterior belief and the Bayes factor are not the same.
The Bayes factor
can be used as evidence, although these categories are arbitrary. Statistical evidence refers to a change in conviction concerning a hypothesis
Summaries and study services for Psychology Bachelor 1 at the University of Amsterdam
On this page study materials for the study Psychology Bachelor 1, University of Amsterdam (UvA), are bundled.
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Statistics, the art and science of learning from data by A. Agresti (fourth edition) – Chapter 3 summaryTHE ASSOCIATION BETWEEN TWO CATEGORICAL VARIABLES
When analysing data the first step is to distinguish between the response variable and the explanatory variable. The response variable is the outcome variable on which comparisons are made. If the explanatory variable is categorical, it defines the groups to be compared with respect to values for the response variable. If the explanatory variable is quantitative, it defines the change in different numerical values to be compared with respect to values for the response variable. The explanatory variable should explain the response variable (e.g: survival status is a response variable and smoking status is the explanatory variable).
An association exists between two variables if a particular value for one variable is more likely to occur with certain values of the other variable.
A contingency table is a display for two categorical variables. Conditional proportions are proportions which formation is conditional on ‘x’. A conditional proportion should be conditional to something. A conditional proportion is also a percentage. The proportion of the totals (e.g: percentage of total amount of ‘no’) is called a marginal proportion.
There is probably an association between two variables if there is a clear explanatory/response relationship, that dictates which way we compute the conditional proportions. Conditional proportions are useful in determining if there’s an association. A variable can be independent from another variable.
THE ASSOCIATION BETWEEN TWO QUANTITATIVE VARIABLES
We examine a scatterplot to study association. There is a difference between a positive association and a negative association. If there is a positive association, x goes up as y goes up. If there is a negative association, x goes up as y goes down.
Correlation describes the strength of the linear association. Correlation (r) summarizes th direction of the association between two quantitative variables and the strength of its linear trend. It can take a value between -1 and 1. A positive value for r indicates a positive association and a negative value for r indicates a negative association. The closer r is to 1, the closer the data points fall to a straight line and the stronger the linear association is. The closer r is to 0, the weaker the linear association is.
The properties of the correlation:
The correlation r can be calculated as following:
N is the number of points. 
and ȳ are means and 
Statistics, the art and science of learning from data by A. Agresti (fourth edition) – Chapter 12 summaryMODEL HOW TWO VARIABLES ARE RELATED
A regression line is a straight line that predicts the value of a response variable ‘y’ from the value of an explanatory variable ‘x’. The correlation is a summary measure of association. The regression line uses the following formula:
The data is plotted before a regression line is made, because it can be strongly influenced by outliers. The regression equation is often called a prediction equation. The difference between y - ŷ, between an observed outcome y and its predicted value ŷ is the prediction error, called the residual. The average of the residuals is zero. The regression line has a smaller sum of squared residuals than any other line. It is called the least squares line. The population regression equation has the following formula:
This formula is a model. A model is a simple approximation for how variables relate in a population. The probability distributions of y values at a fixed value of x is a conditional distribution (e.g: the means of annual income for people with 12 years of education).
DESCRIBE STRENGTH OF ASSOCIATION
Correlation does not differentiate between response and explanatory variables. The formula for the slope uses the correlation and can be calculated as following:
Using this formula, the y-intercept can be calculated:
The slope can’t be used to determine the strength of the association, because it determines on the units of measurement. The correlation is the standardized version of the slope. The formula for the correlation is the following:
A property of the correlation is that at any particular x value, the predicated value of y is relatively closer to its mean than x is to its mean. If a particular ‘x’ value falls 2.0 standard deviations from the mean with a correlation of 0.80, then the predicted ‘y’ is ‘r’ times that many standard deviations from its mean, so the predicted ‘y’ would be 0.80 times 2.0 standard deviations from the mean. The predicted ‘y’ is relatively closer to its mean than ‘x’ is to its mean. This is regression toward the mean. If the first observation is extreme, the second observation will be more toward the mean and will be less extreme.
Predicting ‘y’ using ‘x’ with the regression equation is called the residual sum of squares and this uses the following formula:
The measure r squared is interpreted as proportional reduction in error (e.g: if r squared = 0.40, the error using y-hat to predict y is 40% smaller than the error using y-bar to predict y). The formula for r squared
.....read more Statistics, the art and science of learning from data by A. Agresti (fourth edition) – Chapter 14 summaryONE-WAY ANOVE: COMPARING SEVERAL MEANS
The inferential method for comparing means of several groups is called analysis of variance, also called ANOVA. Categorical explanatory variables in multiple regression and in ANOVA are referred to as factors, also known as independent variables. An ANOVA with only one independent variable is called a one-way ANOVA.
Evidence against the null hypothesis in an ANOVA test is stronger when the variability within each sample is smaller or when the variability between groups is larger. The formula for the F (ANOVA) test is:
When the null hypothesis is true, the mean of the F-distribution is approximately 1. If the null hypothesis is wrong, then F>1. This also increases if the sample size increases. The larger the F-statistic, the smaller the P-value. The F-distribution has two degrees of freedom values:
and 
The ANOVA test has five steps:
If the sample sizes are equal, the within-groups estimate of the variance is the mean of the g sample variances for the g groups. It uses the following formula:
If the sample sizes are equal, the between-groups estimate of the variance uses the following formula:
The ANOVA F-test is robust to violations if the sample size is large enough. If the population sample sizes are not equal, the F test works quite well as long as the largest group standard deviation is no more than about twice the smallest group standard deviation. Disadvantages of the F-test are that it tells us whether groups are different, but it does not tell us which groups are different.
ESTIMATING DIFFERENCES IN GROUPS FOR A SINGLE FACTOR
The F-test only tells us if groups are different, not how different and which groups are different. Confident intervals can. A confidence interval for comparing means uses the following formula:
The degrees of freedom for the confidence interval is:
If the confidence interval does not contain 0, we can infer that the population means are different. Methods that control the probability that all confidence intervals will contain the true differences in means are called multiple comparison methods. Multiple comparison methods compare pairs of means with a confidence level that applies simultaneously to the
.....read more Statistics, the art and science of learning from data by A. Agresti (fourth edition) – Chapter 15 summaryCOMPARE TWO GROUPS BY RANKING
Nonparametric statistical methods are inferential methods that do not assume a particular form of distribution (e.g: the assumption of a normal distribution) for the population distribution. The Wilcoxon test is the best known nonparametric method. Nonparametric methods are useful when the data are ranked and when the assumption of normality is inappropriate.
The Wilcoxon test sets up a distribution using the probability of each difference of the mean rank. This test has five steps:
The sum of the ranks can also be used, instead of the mean of the ranks. When conducting the Wilcoxon test, a z-test can also be conducted if the sample is large enough. This z-test has the following formula:
A Wilcoxon test can also be conducted by converting quantitative observations to ranks. The Wilcoxon test is not affected by outliers (e.g: an extreme outlier gets the lowest/highest rank, no matter if it’s a bit higher or lower than the number before that). The difference between the population medians can also be used if the distribution is highly skewed, but this requires the extra assumption that the population distribution of the two groups have the same shape. The point estimate of the difference between two medians equals the median of the differences between the two groups. A sample proportion can also be used, by checking what the proportion is of observations in group one that’s better than group two. If there is a proportion of 0.50, then there is no effect. The closer the proportion gets to 0 or 1, the greater the difference between the two groups.
NONPARAMETRIC METHODS FOR SEVERAL GROUPS AND FOR MATCHED PAIRS
The test for comparing mean ranks of more than two groups is called the Kruskal-Wallis test. This test has five steps:
The test statistic has an approximate chi-squared distribution with g-1 degrees of freedom. It is
.....read more Research Methods & Statistics – Bayesian statistics summary (UNIVERSITY OF AMSTERDAM)Probability refers to the proportion of occurrence when a particular experiment is repeated infinitely often under different circumstances. It is a long-term relative frequency, does not apply to unique events and is dependent on the reference category.
Subjective probability refers to the subjective degree of conviction in a hypothesis. Objective probability refers to the long-term relative frequency and is the same probability used in classical statistics.
The p-value is the probability of finding a test statistic at least as extreme as the one observed, given that the null hypothesis is true. An X% confidence interval for a parameter is an interval that in repeated use has an X% chance to capture the true value of the parameter. The p-values are only concerned about the null hypothesis, although it is not possible to make statements about the probability of a hypothesis in classical statistics.
If the null hypothesis is true, then the p-values drift randomly. Therefore, it is possible that the p-value is significant by chance. This is why stopping rules are imperative in classical statistics. In Bayesian statistics, the Bayes factor does not drift randomly but drifts towards the correct decision.
In classical statistics, the stopping rules (1), the timing of explanations (posthoc test or not) (2) and multiple tests influence the conclusion. This is not the case in Bayesian statistics.
Classical statistics does not allow for probabilities to be assigned to hypotheses or parameters, whereas Bayesian statistics does allow this.
Bayesian statistics is a method of learning from prediction errors. It assumes that probability does not exist but only uncertainty, which has to be quantified in a principled manner. Therefore, in Bayesian statistics, probability can be assigned to a single hypothesis.
The data drive an update from prior knowledge to posterior knowledge. This method investigates whereas classical statistics investigates .
The Bayes factor can also be seen as the predictive updating factor for the posterior belief. It is the ratio of likelihoods. The likelihood refers to the probability of obtaining the data given the hypothesis. Bayesian statistics use Bayes rule:
The prior distribution determines the posterior distribution, therefore, a high predictive updating factor in favour of the alternative hypothesis does not necessarily mean that the alternative hypothesis is better. It only predicts the dataset X times better than the null hypothesis in this case.
The posterior belief and the Bayes factor are the same if the prior belief is that the distribution is 50/50. Otherwise, the posterior belief and the Bayes factor are not the same.
The Bayes factor can be used as evidence, although these categories are arbitrary. Statistical evidence refers to a change in conviction concerning a hypothesis
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Thanks for sharing this, the Marg00t contributed on 01-06-2021 12:49
Thanks for sharing this, the graphics help out a lot!
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