Correlation and Hypothesis testing - Ryan Ward

Question 1

what is correlation?

Answer 1

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.

Question 2

what can serve as the basis for well-designed experiments

Answer 2

correlation

Question 3

Brazelton Neonatal Behavioural Assessment Scale

Answer 3

women smoking during regency
children did worse on some scales

Question 4

Bower (2020) anxiety in women

Answer 4

found level of anxiety in pregnant women and likelihood of premature birth or low birth weight of baby
example of correlation

Question 5

positive correlation and how it can be represented

Answer 5

as one variable gets bigger the other variable gets bigger can be represented on a scatter plot
tilts upward from Left to Right

Question 6

negative correlation and how it is represented

Answer 6

as one variable gets bigger the other variable gets smaller
tilts down on scatter plot from Left to Right

Question 7

zero correlation and how its represented

Answer 7

no consistent relation between variables
scattered points with no patter

Question 8

Correlation in terms of strength

Answer 8

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

Question 9

way to compute correlation is Pearson R what is this

Answer 9

slope of line that minimises difference between line and each point
used by psychologists

Question 10

3 things to know about R

Answer 10

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

Question 11

linear

Answer 11

points that generally fall on a straight line

Question 12

if r = 0 or is low it means

Answer 12

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

Question 13

curvilinear

Answer 13

increase the x results initially in increase in y, then decrease in y

Question 14

example of curvilinear

Answer 14

Yerkes-Dodson arousal curve

Question 15

Yerkes-Dodson arousal curve

Answer 15

describes the relationship between arousal and performance. It suggests that there is an optimal level of arousal for achieving peak performance on a task.

Question 16

Cross-lagged-panel correlation procedure

Answer 16

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.

Question 17

cross-legged-panel correlation underlying assumption

Answer 17

if one variable “causes” the other, it should be more strongly related over time

Question 18

cross-legged-panel correlation general strategy

Answer 18

obtain several correlations over time then look at size and direction of the correlation coefficients to determine what leads to what

Question 19

inferential statistics

Answer 19

iued to decide about the population based on observations of the sample

Question 20

characteristics of population and the symbols

Answer 20

parameteres:
μ mean and σ standard deviation
can’t measure the entire pop so use sample

Question 21

characteristics of sample the symbols for them

Answer 21

statistics:
X̄ mean and s standard deviation

Question 22

3 steps for sampling distributions and logic

Answer 22

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)

Question 23

central limit theorem

Answer 23

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.

Question 24

sampling distribution

Answer 24

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

Question 25

if the likelihood is very small that the results could have been obtained from the distribution suggested by Ho

Answer 25

then reject the null hypothesis in favour of the alternate hypothesis – if p is low reject Ho

Question 26

if the observed mean (X̄) could have reasonably been obtained from the distribution suggested by Ho (due to chance variation) then

Answer 26

retain (never accept the null hypothesis) the null hypothesis

Question 27

what is the null hypotheses (Ho)

Answer 27

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.

Question 28

what is the alternative hypothesis (H1)

Answer 28

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.

Question 29

significance level or alpha (α) level

Answer 29

the probability value that defines the boundary between rejecting or retaining the Ho

if p is less than alpha then you reject the Ho

Question 30

what is the significance level usually set at for psychologists

Answer 30

0.05 or sometimes 0.01
p < .05

Question 31

Region of rejection

Answer 31

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

Question 32

when is a one-tailed test used

Answer 32

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

Question 33

when is a two-tailed test used

Answer 33

when we have a non-directional alternative
eg. something could improve or worsen memory

two directional could do either

Question 34

critical value

Answer 34

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

Question 35

type 1 error

Answer 35

This is the error of rejecting the null hypothesis when it is true. It represents a false positive result.

Question 36

type 2 error

Answer 36

This is the error of failing to reject the null hypothesis when it is false. It represents a false negative result.
p = beta

Question 37

use a two-tailed test unless there is what

Answer 37

a “good” (theoretical reason) to use a one-tailed one

Question 38

what are decision errors and what are the two types

Answer 38

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.

Question 39

what does it mean that type | and type || errors are mutually exclusive

Answer 39

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

Question 40

two ways to minimise type || errors

Answer 40

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

Question 41

what effect does increasing alpha have in order to minimise type 2 error

Answer 41

increasing alpha also produces a higher probability of a Type 1 error (rejecting the null when it is true)

Question 42

when to set alpha high or low

Answer 42

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

Question 43

by increasing sample size to minimise type 2 error

Answer 43

has less variability
narrower sampling distribution
reduced β (alpha doesn’t change)

Question 44

single sample t-test

Answer 44

used to test the null hypothesis for a single-sample experiment when the standard deviation of the population must be estimated

Question 45

two sample t-test

Answer 45

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.

Question 46

degrees of freedom is

Answer 46

how many scores in the sample are free to vary - generally all scores except the last one

Question 47

assumptions of the single-sample t-test

Answer 47

1. the random sample compromises interval or ratio scores (directly comparable quantitative rather than ordinal)
2. the distribution of the individual scores is normal
3. that standard error of the mean is estimated using ^sx computed from the sample

Question 48

student t-test

Answer 48

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.