Correlation and Hypothesis testing - Ryan Ward Flashcards
what is correlation?
refers to a statistical measure that quantifies the relationship or association between two variables. It indicates the extent to which changes in one variable are systematically related to changes in another variable.
what can serve as the basis for well-designed experiments
correlation
Brazelton Neonatal Behavioural Assessment Scale
women smoking during regency
children did worse on some scales
Bower (2020) anxiety in women
found level of anxiety in pregnant women and likelihood of premature birth or low birth weight of baby
example of correlation
positive correlation and how it can be represented
as one variable gets bigger the other variable gets bigger can be represented on a scatter plot
tilts upward from Left to Right
negative correlation and how it is represented
as one variable gets bigger the other variable gets smaller
tilts down on scatter plot from Left to Right
zero correlation and how its represented
no consistent relation between variables
scattered points with no patter
Correlation in terms of strength
strong = close to the centre line IV predicting DV stronger
weak = something else is probably going on as well as correlation causing dots to be further from the centre line
the stronger the correlation the better the predictability
way to compute correlation is Pearson R what is this
slope of line that minimises difference between line and each point
used by psychologists
3 things to know about R
variables to be correlated must be measured on the same individuals
variables must be measured on an interval or ratio scale
r can detect only linear relationships
linear
points that generally fall on a straight line
if r = 0 or is low it means
it may be that there is no relationship or it may ne that the existing relationship is non-linear
may be because of a restricted range - need a certain amount of spears or variability in scores
curvilinear
increase the x results initially in increase in y, then decrease in y
example of curvilinear
Yerkes-Dodson arousal curve
Yerkes-Dodson arousal curve
describes the relationship between arousal and performance. It suggests that there is an optimal level of arousal for achieving peak performance on a task.
Cross-lagged-panel correlation procedure
A way of dealing with the directionality problem to a certain extent
It is commonly used in longitudinal research to explore the temporal order of variables and investigate potential causal relationships.
cross-legged-panel correlation underlying assumption
if one variable “causes” the other, it should be more strongly related over time
cross-legged-panel correlation general strategy
obtain several correlations over time then look at size and direction of the correlation coefficients to determine what leads to what
inferential statistics
iued to decide about the population based on observations of the sample
characteristics of population and the symbols
parameteres:
μ mean and σ standard deviation
can’t measure the entire pop so use sample
characteristics of sample the symbols for them
statistics:
X̄ mean and s standard deviation
3 steps for sampling distributions and logic
make a guess about the population frequency distribution - hypothesis what pop mean is
take a random sample
decide if sample came from a pop, like the one you guessed in step 1 (usually based on how close sample mean is to the hypothesised pop mean)
central limit theorem
take enough samples with means always get a normal distribution
when independent random variables are summed or averaged, regardless of their underlying distribution, their sum or average tends to follow a normal distribution as the sample size increases.
sampling distribution
When we take a single random sample from a population and calculate a statistic, such as the sample mean, we obtain a single value. However, if we were to take multiple random samples of the same size from the population and calculate the statistic for each sample, we would end up with a distribution of those statistics. This distribution is called the sampling distribution.
whether the difference in sample and pop is due to chance or something real based on variability and true difference
if the likelihood is very small that the results could have been obtained from the distribution suggested by Ho
then reject the null hypothesis in favour of the alternate hypothesis – if p is low reject Ho
if the observed mean (X̄) could have reasonably been obtained from the distribution suggested by Ho (due to chance variation) then
retain (never accept the null hypothesis) the null hypothesis
what is the null hypotheses (Ho)
statement that asserts that there is no significant relationship or difference between variables or populations.
a position of no effect, no difference, or no relationship. It assumes that any observed differences or relationships in the data are due to chance or random variation rather than a true underlying effect.
what is the alternative hypothesis (H1)
statement that contradicts or opposes the null hypothesis (Ho). It represents the possibility of a significant relationship, difference, or effect between variables or populations that is not due to chance or random variation.
significance level or alpha (α) level
the probability value that defines the boundary between rejecting or retaining the Ho
if p is less than alpha then you reject the Ho
what is the significance level usually set at for psychologists
0.05 or sometimes 0.01
p < .05
Region of rejection
The region of rejection represents the range of values of the test statistic that would be unlikely to occur by chance alone if the null hypothesis were true. If the calculated test statistic falls within this region, it suggests that the observed data are inconsistent with the null hypothesis, providing evidence for the alternative hypothesis.
if number is in region of rejection - reject Ho
when is a one-tailed test used
when we have a directional alternative
eg something improving memory
used when there is evidence or theory to suggest that the treatment will have an effect in one particular direction
when is a two-tailed test used
when we have a non-directional alternative
eg. something could improve or worsen memory
two directional could do either
critical value
specific value or set of values that define the boundaries of the region of rejection in hypothesis testing. It is used to make decisions about whether to reject or fail to reject the null hypothesis based on the observed test statistic.
z = critical value
type 1 error
This is the error of rejecting the null hypothesis when it is true. It represents a false positive result.
type 2 error
This is the error of failing to reject the null hypothesis when it is false. It represents a false negative result.
p = beta
use a two-tailed test unless there is what
a “good” (theoretical reason) to use a one-tailed one
what are decision errors and what are the two types
refer to the incorrect conclusions that can be made when performing a statistical test. There are two types of decision errors: Type I error and Type II error.
what does it mean that type | and type || errors are mutually exclusive
if you have one you can’t have the other
changes in one type of error have an effect on the other type of error
two ways to minimise type || errors
reducing beta and increasing power (1-β) so that we can reject the null hypothesis when it is false
increase alpha
increase sample size
use most powerful statistical test
have a good experimental design
what effect does increasing alpha have in order to minimise type 2 error
increasing alpha also produces a higher probability of a Type 1 error (rejecting the null when it is true)
when to set alpha high or low
set alpha very low (0.01) when consequences of type 1 error are severe
set alpha high (0.05) when consequences of type 1 errors are not too serious
by increasing sample size to minimise type 2 error
has less variability
narrower sampling distribution
reduced β (alpha doesn’t change)
single sample t-test
used to test the null hypothesis for a single-sample experiment when the standard deviation of the population must be estimated
two sample t-test
used to compare the means of two separate groups and determine if they are significantly different from each other. It helps assess whether there is a significant difference between the means of two populations.
degrees of freedom is
how many scores in the sample are free to vary - generally all scores except the last one
assumptions of the single-sample t-test
- the random sample compromises interval or ratio scores (directly comparable quantitative rather than ordinal)
- the distribution of the individual scores is normal
- that standard error of the mean is estimated using ^sx computed from the sample
student t-test
is a statistical test used to compare the means of two groups and determine if they are significantly different from each other. It is commonly used when the sample sizes are small or when the population standard deviation is unknown.
