Quantitative approaches, unit 3

What is statistical inference

• Drawing conclusions from data where a full picture may not be available

• Logical deduction from the available evidence

What is the frequentist approach

Assesses the likelihood of an event based on long term frequency of occurence

What is the bayesian approach

Updates the probability of a hypothesis as more evidence becomes available

Describe the frequentist approach (objective statistics)

• Involve making decisions (interpretation)

• Can not tell us about the ‘truth’ of an experiment but helps to determine pribability

• Often seen as more objective as they rely on observed data and do not involve subjective prior distribution

• Widely accepted, long established

• Not suited for small samples

• Emphasizes hypothesis testing, uses p values to assess the evidence against a null hypothesis

Describe the Bayesian approach (subjective statistics)

• Updating beliefs about the world

• A mathematical approach that evaluates to what extent we should change/update our current belief based on new evidence or information

• Incorporates prior beliefs therefore subjective

• Suitable for small sample sizes as bayesian methods assign degrees of belief (known as posterior probabilities) to hypotheses, suitable as prior knowledge is incorporated into the analysis

What is null hypothesis significance testing (NHST)

• Uses frequential statistical inference

• Allows you to ask the question ‘can i reject the null hypothesis with a desired error rate’

• Researchers test the null hypothesis with a desired long run error rate (alpha a)

What are the decision outcomes of null hypothesis signifiance testing (NHST)

• Failure to reject the null (IV did not have an effect), no statistically significant difference

• Rejecting the null (IV did have an effect), there was a statistically significant difference

What is an error rate

A threshold that helps us to interpret our results, if our results have a low probability of occuring under the null hypothesis, we reject it

What is a p value

• The probability of observing the sample date,

• Assuming the null hypothesis is true#

• Helps us decide if our findings are unexpected n the context of the null hypothesis being true

What is alpha a criterion

• The cut off point

• 0.05

• If p value is <a then null hypothesis is rejected and alternative hypothesis is accepted

• If p value >a, null hypothesis can fail to be rejected and alternative hypothesis is not accepted

What is a type I error

• False positive

• Occurs when an investigator rejects a null hypothesis that is actually true within the population

• eg convicting someone of a crime when they are actually innocent

What is a type II error

• False negative

• When investigator fails to reject a false null hypothesis that is actually false within the population

• eg acquitting a guilty individual when they are guilty of a crime

What is statistical power

• The likelihood that a study will detect an efffect or difference when it truly exists

• Represents the ability of a statistical test to correctly identify a real effect (minimizes the chances of a false negative)

• High statistical power is desirable because it increases reliability of research findings

What is the type I error rate

Alpha

What is the type II error rate

Beta

What factors influence power

• Sample size, bigger samples tend to have more power, making it easier to see real effects

• Effect size, the stronger the effect size, the easier it is to detect

• Significance level, choosing a standard eg 0.05 means you’re more likely to find true effects

What is the relationship between p (probability value) and N (sample size)

Even the smallest effect will become statistically significant if you test enough people

How does large sample size influence relationship between p and N

• The t test becomes more sensitive to detecting smaller differences or effects (if you test enough people, even a tiny effect will become significant, which may have little real world importance)

• The standard error of the mean decreases, making the t statistic more precise

• The increased precision often results in smaller p values, as the sample mean becomes a more reliable estimate of the population mean

How does small sample size influence relationship between p and N

• A t test is less sensitive with smaller samples as it may have reduced power to detect smaller effects

• The standard error of the mean is larger for smaller samples, leading to a precise estimate of the population mean

• Consequently, p values may be larger, making it harder to achieve statistical significance, especially for small effect sizes

What is effect size

• Quantifies the magnitude of a difference or relationship observed in a study between treatment group and control group

• Absoloute effect size measures difference between two groups

What is a common standardized effect

Cohen d

What is a small, medium and large effect size

• Small, 0.2

• Medium, 0.5

• Large, 0.8

How is p (p value), n (sample size), effect size and power related

• Size of effect is related to how many participants will be needed to demonstrate the presence of a statistically significant effect (if it exists)

• Effect size is determined via smallest effect size of interest

• Greater sample sizes are able to detect statistically smaller effects

• Power of statistical test is the probability that the test will be able to detect a statistical difference from null hypothesis

What is an effect moderator

Represents conditions eg gender, for which the magnitude of an effect an IV has on a DV will be different

What is a mediating variable

• Variables considered to be in between IV and DV and form a causal chain

• Independent to mediator to DV

What is a confounder variable

Extraneous variables interfering with the interpretation of a causal relationship between IV and DV

What is experimental research

• Compaing 2 or more groups that are similiar except for one factor or variable

• Conditions are highly controlled and variables manipulated by researcher

What is applied behaviour analysis

• Very similiar to a singular case study

• One person, examines the individuals responses in different situations (conditions) across time

What happens if normality assumptions are not met

• You use alternative non parametric tests in place of parametric tests

• Eg Mann Whitney, Wilcoxon, Kruskal Wallis

• These tests rank data

Difference between parametric and non parametric test

• Parametric, assume a specific population distribution (usually normal) and use parameters eg mean

• Non parametric tests make no distributional assumptions and typically use medians or ranks instead

What is skewness

• The measure of symmetry or the lack of symmetry

• A data set is symmetric if it looks the same to the left and right of the centre point

What is Kurtosis

• A measure of whether the data is peaked or flat relative to a normal distribution

• Data sets with low kurtosis tend to have a flat top near the mean rather than a sharp peak

When is chi square test applicable

• Used to see if 2 categorical variables are related

• Uses the sum of squared differences between each pair of observed and expected values