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bivariate correlation
An association that involves exactly two variables.
Association claim
Describes the relationship found between 2 measured variable.
Correlational studies
A study is correlational if it has two measured variables
-Construct validity - how well was each variable measured, good reliability? measuring what it intends to measure? Evidence for face validity? Concurrent validity (how well it agrees with other “Gold standards”)? Convergent (how well it correlates with other measures of similar constructs) vs discriminant validity (ensures that a measurement tool is distinct from other measures assessing different constructs)?
-external validity → to whom can the association be generalized?
-internal validity → can we make a causal inference from an association?
-Statistical validity → How well does data support the conclusion? Point estimate - the value that is the result of your analysis
How strong is the relationship?
effect size r - describes the strength of the relationship
In a stronger effect size, r is closer to 1/-1
can indicate the importance of a result
with all else equal, larger effect sizes are more important
small effect sizes can still be important/ can compound over many observations
can be aggregated over many situations and many people.
How precise is the estimate?
Confidence intervals
designed to include the true population value a high percentage of the time (usually 95%)
If it does not include 0, relationship is statistically significant
If it does include 0, relationship is not significant
SMALL SAMPLES = WIDER CI’s (less precise)
LARGER SAMPLES = narrower CI’s (more precise)
Has it been replicated?
If a result can be replicated we can be more confident about the association.
Could outliers be affecting the association?
Outlier
an extreme score; a single case that stands out from the rest of the data
can make correlations appear stronger/weaker
outliers can exert disproportionate influence
in bivariate correlation → outliers are mainly problematic when they have extreme values on both variables
outliers are more problematic in small sample sizes bc they have more influence
Is there restriction of range?
Restriction of Range
when there is not a full range of scores on one of the variables in the association
can make correlation appear smaller/weaker
ex: SAT scores- most colleges look at 1200-1600 scores (restricted)
only using a partial range underestimates true correlation
similar to floor/ceiling effects
we msut ask about it when correlations appear weaker than expected
how do researchers correct this
obtain full ranges, then compute the correlation
correction for restriction of range→ Statistical formula to correct for the error
Is the association curvilinear
Curvilinear association
The relationship between two variables is not a straight line + than -
correlation coefficient close to 0
detect using scatter plots, r values will not describe data well
directionality problem
the difficulty in determining which variable influences the other when a correlation is observed, as it's impossible to conclude whether variable X causes Y or vice versa.
Internal validity and association claims
not necessary to interrogate internal validity for an association claim but we need to protect ourselves from the temptation to make a causal inference
potential 3rd variables can explain a bivariate association → SPURIOUS CORRELATION
must correlate with both variables in the association
External Validity and association claims
To whom can the association be generalized
for this, size of sample does not matter as much as the way the sample was selected from the people of interest
moderator: a variable that influences the relationship between 2 other variables
example: pro sports team wins vs. attendance - dependent on the moderator of whether the city has low or high residential mobility.
Variables
How to operationalize them, how to describe their type and scale, how to interrogate construct validity
Association
How to describe and plot them, how to interrogate statistical validity
Reasons experiments support causal claims
1) COVARIANCE - do the results show that the causal variable is related to the outcome variable? Are distinct levels of IV associated with different levels of DV?
2) TEMPORAL PRECEDENCE - Does the study design ensure that the causal variable comes before the outcome variable in time?
3) INTERNAL VALIDITY - Does study rule out alternative explanations for the results?
3 types of comparison groups
control group →a level of IV intended to represent “no treatment”
treatment group → Participants in an experiment exposed to the level of IV that involves medication or the experimental condition
placebo group → group exposed to an inert treatment such as a sugar pill
Selection effect
when the kinds of participants in one condition are systematically different from those in the other
IF THERE IS SYSTEMATIC VARIATION WE CANNOT MAKE A CAUSAL CLAIM REGARDING THE IV AND DV
random assignment
helps to avoid selection effects - flip a coin to assign groups
matched groups
participants were sorted form lowest to highest on some variable, then grouped into sets of 2, so two participants with the highest score were in different groups,D and then so on and so forth. Then each group is randomly assigned to an experimental group.
Design Confound
Essentially, an alternative explanation. another variable that varies systematically with IV
a variable is only a confound when its levels vary systematically across levels of IV
systematic variability
changes in a dependent variable that are consistently related to the independent variable or other factors, rather than random fluctuations
BETWEEN GROUPS
BAD FOR INTERNAL VALIDITY
unsystematic variability
random, unpredictable fluctuations or differences in data that are not explained by the independent variables being studied WITHIN GROUPS
NOT A THREAT TO INTERNAL VALIDITY
problematic for statistical power, might see a null
EXPERIMENT
Researchers manipulate at least one variable and measure another.
Independent groups
different participants at different levels of IV
2 basic subtypes
posttest only →DV measured once after manipulation of IV
pretest/posttest →DV measured before and after manipulation of IV
both use random assignment
WHICH IS BETTER - IT DEPENDS
in some situation its problematic to use pre/post → if DV will cause fatigue or familiarity effects
posttest only can still be very powerful - random assignment and manipulation of IV
Within groups
same participants undergo all levels of IV
2 basic subtypes
concurrent → all levels of the IV are experiences at once SIMULTANEOUSLY (DV is preference)
repeated measures → levels of IV are experienced sequentially ONE AFTER THE OTHER (condition 1→measure dv- constion 2 - measure dv)
ADVANTAGES
no selection effects - groups are equivalent
unsystematic variability is less of a problem since participants are being compared to themselves.
statistical power- increased ability to detect between conditions
need fewer participants!
DISADVANTAGES
order effects (a potential compound)
might not be practical/possible
demand characteristics- participants an act in different ways based on knowledge of the IV
Order effects
exposure to 1 level of IV can influence responses to subsequent levels of IV
a confound because differences in DV may be explained by the sequence in which the levels were experienced
Counterbalancing
Used to avoid order effects
full counterbalancing → all orders, combinations used
partial counterbalancing → not all orders are tested
Practice effects/fatigue effects
participants may get better as a task continues OR get tired or bored towards the end.
Carryover effects
some form of contamination carries over from one condition to the next
Causal claim construct validity
How well was the DV measured
How well was IV manipulated
manipulation check - an extra dependent variable that researchers insert into an experiment to convince them that their experimental manipulation worked.
pilot studies - a simple study with a separate group of participants completed before the main study to confirm the effectiveness of a manipulation.
causal claim external validity
To whom or what can the causal claim generalize
to other people/ situations
If external validity is poor? not as much a concern of internal validity, this work can be done in future experiments
causal claim statistical validity
How much? How precise? How large is the effect? Is it significant? Has study been replicated?
causal claim internal validity
Are there alternative explanations for the results
were there design confounds
if independent group design was used, did researchers control for selection effects using random assignment or matching groups?
If the within-group design was used, did researchers control for order effects by counterbalancing
Null effects
The IV does not make a significant difference in the DV (the 95% CI includes 0)
What does it mean if the IV does not make a difference
it can mean…
not enough between groups variability
too much within groups variability
really no true difference
5 reasons for not enough between groups variability
1) Weak manipulations → The difference between IV levels is too small to be meaningful
2) Insensitive measures → operationalization of the DV does not have enough sensitivity to detect a difference between levels of the IV - should use detailed quantitative increments
3) Ceiling and Floor effects
ceiling effect: scores squeezed at top end of DV scale
floor effect: scores are squeezed together at bottom end of DV scale
Can be the result of problematic IV or DV
4) manipulation checks → additional dependent measure added to a study that can reveal a weak manipulation resulting in ceiling/floor effects
5) design confounds acting in reverse → confounds usually threaten internal validity, but they can also apply to null effects
Too much within groups variability
A null effect could arise due to this
unsystematic variability is not a problem for internal validity, but it can make it harder to find a true difference between conditions
CAUSES
measurement error
individual differences
situation noise
Measurement error
a human or instrument factor that can randomly inflate or deflate a person’s score on the DV
all DV’s involve a certain amount of measurement error
researchers try to keep these errors as small as possible
a groups’ mean on a DV will reflect the true mean ± random measurement info
when distortions od measurement are random they cancel out and do not affect the group mean
but a lot of measurement errors will result in more “spread out scores” making it harder to detect a difference between groups
Solutions
use reliable, precise measurements
measure more instances
Individual differences
differences across participants that add variability in DV scores
solutions
change the design →use a within-groups design to accommodate for individual differences
add more participants → less impact from any single participant
Situation noise
any kind of external distraction that could cause variability within groups that obscure between-group differences
can be minimized by controlling the surroundings of an environment
95% Confidence intervals and precision
can have a narrower CI (more precise) by…
dec error variability by using precise measurements, reducing situation noise or studying only one type of animal/person
inc sample size
In a 95% CI, constant is at least 1.96
If variability is low and sample size is high and we have a null effect…
The IV could have almost no effect on DV
The IV could have a true effect on DV but because of random errors or measurement or sampling, this one study didn’t detect it
Power
The likelihood that a study will yield a statistically significant result when the IV really has an effect
statistical power leads to more precise estimates,
can be improved with…
within groups design
strong IV manipulation
a large sample size
less within groups variability
Advantages of large samples
inc statistical power, resulting in more precise estimate, narrowing CI, easier to detect true effect
small samples are less precise, so they increase the likelihood that you will detect an effect that is not actually there, making it unlikely to replicate
Null effects are published less often
can be just as interesting
journals are becoming more likely to publish null research
may be less published in popular media