Correlations and Experiments, Single-factor and factorial designs Flashcards
Pearson’s r
= quantification of a correlational relationship = product-moment correlation coefficient
-> indicates the degree of linear relation between 2 variables
-> varies between -1 and +1
-> absolute value indicates the strength
-> +/- indicates the direction of the correlation
effect size
In statistics, the effect size is a measure that quantifies the strength or magnitude of the relationship between two variables or the magnitude of a difference between groups. It is used to provide a clear and meaningful understanding of the practical significance of a statistical result, as opposed to just the statistical significance. Effect size helps researchers and analysts determine whether an observed effect is large enough to be practically important or meaningful.
significance level
A significance level, often denoted as α (alpha), is a threshold or critical value used in hypothesis testing in statistics. It is a predetermined level of probability that is used to determine whether a statistical result is considered statistically significant or not. In other words, the significance level helps in making decisions about the null hypothesis.
Setting the Significance Level: Before conducting a statistical test, researchers choose a significance level, typically a small value such as 0.05 (5%) or 0.01 (1%). This value represents the maximum allowable probability of making a Type I error, which is the error of rejecting a true null hypothesis (a false positive).
Conducting the Test: After setting the significance level, researchers perform the statistical test, which typically involves comparing sample data to a null hypothesis. The test calculates a p-value, which is the probability of obtaining the observed results (or more extreme results) if the null hypothesis is true.
Making a Decision: If the p-value is less than or equal to the chosen significance level (α), it is considered statistically significant. In this case, researchers typically reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis. If the p-value is greater than α, the results are not considered statistically significant, and researchers do not reject the null hypothesis.
directionality problem
direction of correlation is unknown
third variable problem
a 3rd variable that affects both other variables is present
criteria to establish causation
- Covariance: results must show that variables correlate
- Temporal precedence: method must establish which variable comes first in time
- Internal validity: there must not be a C variable that is associated with variables A and B, independently
cross-lagged panel procedure
The “cross-lagged panel procedure” is a statistical technique used in correlational research to examine the direction of causality between two or more variables over time. It involves analyzing multiple measurements of these variables taken at different points in time and looking for patterns or relationships that suggest the order in which they occur
what if the correlation is 0?
- restriction of range (or truncated range)
- non-linear relationship
- no association
experiment
when a articular comparison is produced while other aspects of the situation are held constant
ceiling effect
test was too easy
floor effect
test was too difficult
reasons for Null results in experiments
- independent variable did not affect dependent variable
- manipulation was too weak
- insensitive measures
- ceiling effect
- floor effect
- unreliable measurement
- not enough power (small N)
experimental designs
How to assign subjects to different levels of the independent variable:
1. Between-subjects design
2. Within-subjects design
Between-subjects design
= independent-groups design
= separate groups of subjects receive different levels of the independent variables
Within-subjects design
= repeated-measures design
= all subjects receive all levels of the independent variables
Between-subjects design: advantages
there is no chance that one level of the independent variable affects performance under the other level of the independent variable
Between-subjects design: disadvantages
there is a chance that the groups differ
-> can be “solved” by random assignment / matching
Between-subjects design: when to use?
- the independent variable has a permanent effect
- large risk of order effects
Within-subjects design: advantages
there is no chance of group differences. each subjects serves as their own control
Within-subjects design: disadvantages
there is a chance of order effects (e.g. practice, carryover)
-> can be “solved” by counterbalancing methods or random order
partial counterbalancing
Partial counterbalancing is used when it’s not feasible to present every possible order to each participant, which can be the case in experiments with a large number of conditions. In partial counterbalancing, a subset of possible orders is used, and this subset is typically determined based on a systematic approach. For example, if you have four conditions (A, B, C, D), you might use a partial counterbalancing scheme like ABDC, CADB, BCAD, DCBA. This method still helps control for order effects but is less comprehensive than full counterbalancing.
Full counterbalancing / Complete counterbalancing
In a full counterbalancing design, every possible order or sequence of conditions is presented to each participant. This means that if you have, for example, three conditions (A, B, and C), each participant experiences all six possible sequences (ABC, ACB, BAC, BCA, CAB, CBA). This ensures that any order or sequence effects are equally distributed across participants, making it possible to isolate the effects of the independent variable from the order in which conditions are presented.
Latin Square Design
A Latin square design is a structured approach to partial counterbalancing. It’s especially useful when you have more conditions than can be easily counterbalanced. In a Latin square design, you have as many rows and columns as you have conditions. Each condition appears once in each row and once in each column. This design ensures that each condition appears in each position an equal number of times. Latin squares are particularly useful when there is a concern about order effects and when full counterbalancing is impractical.
Balanced Latin-Square Design
A balanced Latin square design takes the concept of a Latin square a step further. It ensures that not only do conditions appear equally often in each position but also that each condition appears equally often after every other condition. This design offers a more rigorous control over order effects.
