Statistics: Formulas for Variance and Correlation

"the study of the way cultural traditions and social practices regulate, express, transform, and permute the human psyche..." Shweder (1990)
primarity quantitative

no.levels x sum of (participant mean - grand mean)^2

% of X I can predict using Y or visa versa

(n+1)/2 - find score in this nth position
For even set of numbers, add two middle numbers then divide by two

(X-X^)(Y-Y^) = positive

(X-X^)(Y-Y^) =negative

1

1 - might need subgroups to change orders

1. Calc standard error
2. Use standard error to calc Z score (X)
3.Use Z-score to find decimal on table
4.prob of getting at least a score of X is 1-decimal
5. if probability is <0.05 then the sample is NOT rep of pop

1. estimate the variance of the population of difference scores
2. use this variance to estimate the standard error of the distribution of sample difference scores
3. calculate obtained t-value (the mean difference between the two samples)
4. look up the obtained t-value in the t-table - if the obtained t value is larger than the number printed in the table then the probability of getting a difference that large by chance is less than .05 = reject the null hypothesis

1. grand mean
2. sums of squares
SStotal, SStreatment, SSparticpants, SSrandomerror
3. degrees of freedom
dftotal = total no. scores - 1
dftreatment = no. conditions - 1
dfparticipants = no. participants - 1
dfrandomerror = dftreatment x dfparticipants
3. mean squares
MStreatment
MSrandomerror
4. F ratio
MStreatment/MSrandomerror
5. P value
if F ration is greater than p value = reject null hypothesis

1. order p values from lowest to highest
2. calc a holm's modified alpha level to compare smallest P value against
= alpha/#tests - rank of comparison + 1
3. if p obtained < H alpha reject null hypothesis
4. repeat until p obtained > H alpha
= retain null hypothesis and stop
all comparisons with higher rank retain null hypothesis

1. overall mean
2. sums of squares - SSbetween, SStotal, SSwithin
3. degrees of freedom
dftotal = no. data scores - 1
dfbetween = no. groups - 1
dfwithin = addition of no. in each group - 1
4. mean squares
MSbetween = SSbetween/dfbetween
MSwithin= SSwithin/dfwithin
5. F Ratio
6. P value
7. if F ratio is greater than p value = reject null hypothesis

1.create H0 and H1
2. calc population variance estimated from each sample
3. calc s^2pool for the two sample
4. calc standard error of the distribution of sample means (sx1-x2)
5. calc difference in sample means
6. calc t obtained
7. df on table = (n1-1)+(n2-1)
8. compare t on table with t obtained
9. If t obtained > t on table, reject null hypothesis

100-x = c
find c in mass area of z score table (closest)
find corresponding z score
score = mean + z x sd

>1

a large number of users agree that a measure assesses what it was designed to assess

a measure is a more sensitive predictor of a construct than previous measures

a person's relative standing in a group can be defined by the percentile of their raw score

Acknowledge issues of the path
Should strengthen research capabilities of Aboriginal + TS Islander people and their communities
Need to be led by members of those communities

allows for researchers to study the effects of independent variables that cannot be manipulated

allows research questions to be asked in large samples without the need for testing

alpha = 0.10

answering a research question by looking at natural variation and co-variations between and independent and dependent variable

as long as conditions remain the same, a person should show the same performance on the measure each time they take it

b0 + b1X

better
now remove the individual differences variance from SSwithin

calc pop standard deviation
calc pop standard error
calc t score
df = sample size -1
find corresponding t score at 0.05
if calc t score is greater than found then sample is not drawn from pop

Can be used to study IVs that cannot be manipulated
Often have better face validity

can't infer causality

cause comes before effect
effect only occurs when cause is present
alternative explanations ruled out

chance of correctly rejecting a null hypothesis
1-B

co-varies in the same was as your independent variable, cannot be sure which one is responsible for change in DV

Collected blood and hair samples, physiological and health information of aboriginal people without consent

Completing the first condition can affect the second condition - practice, fatigue, carry-over, sensitisation
solution - counter-balance or randomise condition order

correlational, experimental -between subjects design and repeated measures design, quasi-experimental

Cultural inheritance
Credibility of intent

cultural lens, cognitive biases/heuristics, biased

Cumulative frequency = x/100 x total number of scores

d = difference between group means/ srt s^2pool

decrease the degrees of freedom

Dependent variable measured on interval or ratio scale
Populations are normally distributed
homogeneity of variance
independence of observation

Dependent variable measured on interval or ratio scale
Populations are normally distributed
Homogeneity of variance across levels of IV
Sphericity

Dependent variable measured on interval or ratio scale
populations are normally distributed
Participant scores are related across conditions

Dependent variable measured on interval or ratio scale
Samples are normally distributed
homogeneity of variance
Independence of observations

describe behaviours, predict future behaviours, determine whether relationships are causal, explain mechanisms underlying causal relationships

descriptive
interested in subjectivity
not subjective
tries to establish causality

dfbetween
dftreatment

dfwithin
dfrandomerror

Does a measure give a consistent result as long as the conditions being measured remain the same
test-retest reliability
split-half reliability

Does a measure seem to assess what it's supposed to?
face validity
construct validity
consensual validity
incremental predictive validitiy

double

eliminates the conistent effects of extraneous variables

ensure conditions are counterbalanced

Equitable and respectful engagement
Right to define benefits according to own values and priorities
Respectful discussion to determine where the research process and intended outcomes may not benefit the community

estimate the likelihood that a sample with a given mean is representative of a population with an unknown standard deviation

estimates proportion of variability in scores on a dependent variable that can be explained by variations in the level of the independent variable

Examine the simultaneous influence of two or more independent variables on a dependent variable
independent effects of each IV
see the influence of how the IVs interact with each other to influence DV

extreme scores
restricted range

Fair selection/exclusion/ recruitment of participant
No exploitation of participants
fair access to the benefits of research

falsifiable, not circular, parsimonious, precisely define terms and concepts, does not contain non-scientific ideas or forces

Fewer participants required
because the IV is manipulated by the experimenter it can still show causality as long as participants are randomly chosen

fewer, harder

field work, lab work, archival research

finding participants
experimental confounds

guarantees control over situations, participants & measures

guarantees reflect the real world & may increase participant engagement

holding test conditions as constant as possible e.g. test in a quiet room, standard instructions
balance variables across conditions e.g. testing time of day, experimenter

if range doesn't include zero = reject null hypothesis

If the measure is too easy or too hard then it won't reflect variability in construct across participants

incorrect rejection of the null nypothesis

incorrectly not rejecting the null hypothesis

increase alpha level

increase effect size
increase alpha

increase participant number
match groups based on critical individual characteristics

increases

individual differences
situational variables
measurement errors

inflicting no harm
ensure researchers' accountability

influenced by every score in the data set

Intrinsic value
Respect the privacy, confidentiality and cultural sensitives
Capacity of human beings to make their own decisions

intuition, authority, empiricism

large/ reduce

leptokurtic

Likely benefit of the research must justify any risks of harm or discomfort to participants
minimise risk of harm or discomfort
clarifying with participants potential benefits and risks
Where no likely benefit to participants: Risk to participants should be proportionally lower than what would be ethically acceptable where such likely benefits did exist

mean < median < mode
left tail

mean of Y

mean y - (b1 x mean x)

measure subjectively looks like it would work - "pub test"

mode < median < mean
right tail

no. data points - 2

no. levels in IVA x no. levels of IVB

no. levels of between subjects variable

nominal, ordinal, interval, ratio

normal

percentage of total number of scores at or below each raw score. Standardizes

performance across multiple items on a measure should be positively related e.g. odd vs even numbered items on a quiz

platykurtic (larger standard deviation)
approaches shape of z-distribution as sample size increases
single samples T-test

potential benefit
methods approach
Respect for the participants is not compromised by the aims
qualified personnel and appropriate facilities and resources
based on current literature
conducted honestly

Principle of respect for persons, principle of beneficence, principle of justice

problem of culture
problem of transferability
problem of measurement

produces similar results to other established measures of the same construct

qualitative and quantitative

r (sy/sx)

Random assignment eliminates systematic differences between groups
Independent variable is directly manipulated by researcher
Means any differences between groups on the DV must be due to changes in the IV = causality

reduce the alpha level

Research merit and integrity, justice, beneficence, respect

Respect Knowledge and wisdom
Valuing Biological and genetic resources
Fair and reasonable distribution of benefit

retain null hypothesis - correlation found is no larger than chance

retain the null hypothesis

Rights of people to hold and express different values
Understanding that research has consequences for all involved
Mutual intent and agreement at the outset of any research project
Ensuring trust, openness, and engagement of participants

same group completes all variations

small = .01
medium = .06
large = .14

small =.20
medium = .50
large = .80

solved by grouping data into equal intervals = bins

Some experimental manipulations might be unethical
Random levels of an IV might be impossible

Spirit and Integrity
Cultural Continuity
Equity
Reciprocity
Respect
Responsibility

SStreatment
SSparticipants
SSerror

standard deviations

standard error of the mean

strongest

sub in z score formula
find z score on table
ans x 100 is the percentile

sum of (X-mean X)(Y-mean Y)/number of scores

sum of Zx x Zy / N

T-tests comparing pairs of groups but with adjusted alpha level to make tests more conservative
bonferonni alpha = alpha level/ # comparisons

take advantage of natural variations in a variable

Take two groups, - Randomly divide them into two equal-sized groups into experimental and control group

test homogeneity of variance
want Levene's test to be non-significant
ratio of largest to smallest variance should be no larger than 4:1

test scores, constructs and operational definitions, self report, behavioural measurement, physiological recordings

The extent to which there is a clear relationship between distributions of two variables

the name given to differences or variability in the dependent variable not attributable to the independent variable

the probability of committing at least one type-1 error across a series of statistical tests

The value denotes rank and magnitude of difference, has a true zero point e.g. weight scale

the value denotes rank and magnitude of difference. no true zero and values can be neg

the value denotes ranks

the variance of the samples should be approximately the same

theory, prediction or hypothesis, design a study, data (analyse, summarise), write a report, repeated experiments

there is a 5 percent chance of rejecting a true null hypothesis

total number of scores at or below each raw score
percentile/100 x total no. scores

Understand past experiences were exploitative
Recognise important of personal and collective bonds
Cultural distinctiveness

validity, reliability, appropriateness, ceiling/floor effects

value/number is a label that denotes identity

variability between means increases relative to the variability within groups

variability we know about/can identify

voluntary consent, beneficial to society, otherwise unobtainable, degree of risk not outweigh importance, qualified personnel, participant should be able to end experiment, experimenter has duty of care

Western, Educated, Industrialized, Rich, Democracies
does make a difference e.g. visual perception, ultimatum game

Y = b0 + b1X + e

Z score using standard deviation of X and X-X^