PY2501.5 ~ {Multi-way ANOVA}
multiple ANOVAs
can tell us if there are diff in a DV between 2 or more IVs + if there's an interaction between the 2 [or more]
mixed ANOVA
when you have at least one between IV and at least one within subjects IV. used to analyse data that involves both within-subjects and between-subjects factors
when is a mixed ANOVA commonly used
when researchers want to examine the effects of the multiple IVs on a DV, where some variables involve repreated measurements within the same subjects, and others involve diff groups of subjects
between-subjects factor
variables where different groups of participants are exposed to different conditions. for example, you might have one group exposed to a certain drug treatment and another group exposed to a placebo.
within subjects factor
ariables where the same participants are measured multiple times under different conditions. for example, you might measure a subject’s performance at three different time points or under different task conditions.
step in conducting a mixed ANOVA
define the factors + collect data + check assumptions + run the ANOVA + interpret results + post-hoc tests
check assumptions in a mixed ANOVA
normaity: data should be approx normally distributed
sphericity: variances of diff between levels of within-subjects factor should be equal [tested using Mauchly's test]
independence: groups should be independent of each other
interpret results in a mixed ANOVA
look at main effects and the interaction effect [if it isn't significant it means effecr of one factor depends on the levels of the other factor]
advanatges of Mixed ANOVA
comprehensive - allows you to examine both between + within subjects factors simltaneously, making it ideal for experiments that include repeated measures alongside diff groups
efficiency - reduces the need for separate analyses for between + within subjects factors which can make the interpretation of complex data easier
disadvantages of mixed ANOVA
complexity - requires a careful setup of data and assumptions, making it more complex to perform and interpret compared to simpler ANOVA designs
assumption violation - like sphericity can complicate the analysis, although corrections can be applied
estimated marginal means
the predicted means off a DV for diff levels of an IV in a stats model adjusted for other variables in the model. useful for analysong data with multiple factors to understand the effect of one variable while controlling others
advantages of emms
adjustment of cofounding variables - adjust for others, providing clearer understanding of the effect of each factor
interpretation of interactions - when they are present, help clarify how the effect of one factior changes depending on the level of another
precision - offer more precise understaning of group diff [not affected by raw data's variability]
disadvantages of emms
model complexity - require use of stats models which can be complex
assumptions - assumes that model used appropriately fits data and assumptions are met
potential misinterpretation - without proper understanding, risk of misinterpreting adjusting means
main effects
individual influence of each IV on DV in an experiment, so when there are multiple factors in a model the main effect of a factor represents its overall impact of DV [they do not consider interactions between factors]
what does it mean when CI ranges overlap
the true pop values of those groups might not be significantly diff from each other [suggests that there is no clear evidenceto support substantial diff between groups based on data] so data doesn't provide strong enough evidence to conclude significant distinction
overlap of CI
does not confirm no diff, it's still possible that groups differ but sample size might not be big enough to detect diff with stats sig
what does a large and small overlap show
big - suggests diff between groups naybe not be practically sig so t-tests / ANOVA may still be necessary to check for significance
small - indicates that theres some diff between groups but further analysis [hypothesis testing] would be needed to confirm whether diff is stats sig
no overlap
often considered atrong evidence that groups are sig diff, although stats testing is necessary to confirm result
descriptive stats
summarize + describe the basic feature of the data, give a first glance at the central tendecy, variability and distribution of the variables, helping readers understand the general patterms or characteristics of data
inferential stats
used to draw conclusions about pop based on sample data, typically to test hypotheses, [t-tests + ANOVA + regression + correlation] which evaluate the sig of relationships or diff observed in descriptives data
why does descriptive stats go before inferential
d - gives readers a snapshot of data [provides context + clear summary]
i - explains whether observed patterns / diff are stats meaningful
ensures clarity + guides reader through logical flow of how data analyzed + interpreted
multiple within-subjects ANOVA
repeated measures ANOVA [with multiple factors] where the same participants are exposed to all levels of the IVs [so you can measure changes overtime]
where are repeated measures usefu;
interventions + measuring changes over time [longitudinal] + experimental designs where subject is exposed to all conditions
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