Statistics Flashcards
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What is Cohen’s d
Statistics 6
– A measure of distance between two condition means which takes variability into account
How do you assess difference between 2 conditons.
Statistics 6
- Calculate and compare descriptive statistics
– Means, medians, s.d.’s, confidence intervals - Calculate “effect size” using Cohen’s d
- Use some kind of inferential test based on known probability distributions
What is the range of Cohens d and what can be infered from the value
Statistics 6
0 - 1
* 0.2 = small effect size (around 85% overlap)
* 0.5 = medium effect size (around 67% overlap)
* 0.8 = large effect size (around 53%)
What are we trying to do when we are hypothesis testin for 2 population means
Statistics 6
figuring out if they have significantly different means
How do you calculate sample mean difference
Statistics 6
D = Ma - Mb
Difference = Sample mean A - sample mean B
What would the result be for sample mean difference Assuming the null is true.
statistics 6
The difference between the two means is 0.
There is a population of left handed people and right handed people.
In a task involving throwing darts, what would be a hypothesis that favours left handed people in an independent t-test testing the difference between means in 2 conditions.
S6
Left-handed people will be more accurate in a task involving left-handed dart throwing at a target than right handed people doing the same task
S6
What are the two types of 2 sample T tests and when are they used
s6
– Related (or paired or repeated measures) t-test * Use when participants take part in both conditions WITHIN PARTICIPANTS DESIGN
– Independent t-test * Use when participants perform in only one of the two conditions BETWEEN PARTICIPANTS DESIGN
What is the trick for converting Two paired samples means into one sample
S6
Taking the difference between the paired data
Imagine you have reason to believe that attainment in some school district varies w/ left/right handedness and decide to test this idea.
Data for left:
Mean = 24.00
S.d = 12.20
n = 30
Data for right:
mean = 16.5
s.d = 11.8
n = 30
Decided on hypotheses youre testing against, Work out whether you are using the T or Z score and, and reach a conclusion on your decided hypotheses.
4 mark qustion , do the question
S6
- Unpaired T-test
- root (esea^2 + eseb^2)
- T = 2.42
- as N = 30 for both samples and 2 sample test –> 2N -2 = 58
- 2.42 > 2.392 therefore significant evidence for difference between levels of attainment between lefts & rights
You need to use the table Obvs
What is Correlation
Statistics 7 - Correlation & Pearsons R
relationship between 2 variables
Are correlated variables independent or non-independent
S7
Non-independent
How can causality be inferred from correlation?
S7
Trick question - you cant infer causality from correlation
What is covariance
S7
A measure of how much two variables vary together
What do High covariance and low covariance indicate?
S7
High covariance = scores for one variable change, other variable will also change in a predictable manner
Low covariance = changes in one variable are not accompanied by a predictable change in the other variable
What does positive covariance indicate?
S7
higher than average values of one variable tend to be paired with higher than average values of the other variable
What does negative covariance indicate?
S7
that higher than average values of one variable tend to be paired with lower than average values of the other variable.
What does zero covariance indicate?
S7
if the two random variables are independent, the covariance will be zero
- does not necessarily mean variables are independent, could just be indicative of a non-linear relationship
What is pearsons R
S7
Shared variance/ total variance
what do the scores of pearsons r indicate
0 < r < 1 = imperfect positive correlation
-1 < r < 0 = imperfect negative correlation
R ~ 0 = low correlation
What are the steps of using Null Hypothesis significance testing for pearsons R
S7
1- Formulate hypothesis
Null - no correlation
Research 1 - (1 tailed) there is a positive correlation
Research 2 (1 tailed) there is a negative correlation
Research 3 (2 tailed) there is a correlation (does not commit to a direction)
2 - get data
3 calculate P value
4 - reject null
What does the P value of pearsons R tell you?
S7
the probability that the correlation coefficient could arise by chance assuming the null is true
What are some of the limitations of an extreme Pearsons R?
S7
not tell you there is necessarily a correlation between your variables, it could be really really really unlikely but still occur
What is the difference between a parametrci and non-parametric tests
Statistics 8 - Non parametric hypothesis tests
- Parametric tests make certain important assumptions about populations from which data are sampled
- Non-parametric tests make far fewer assumptions about populations from which data are sampled
What are some of the common testing assumptions of parametric testing.
S8
– Populations from which samples are drawn should be normally distributed
– Variances (s.ds) of the populations should be approximately equal
– No extreme scores (since these have a big impact on the estimated sample statistics)
What are the benefits of using parametric testing if it features so many assumptions
S8
- ## Typically more powerful than other other approaches
Why use non-parametric testsing if its less powerful
S8
– Because sometimes the assumptions of parametric testing are violated
– In this case we can almost always at least try a non- parametric alternative
What are some exmaples of non -parametric tests
S8
- mann- whitney U test
- Wilcoxon signed rank test
- Spearmans Rho
- 2x2 chi square test
- 1 variable chi square test
What is the Mann-Whitney U test
S8
a Non-parametric alternative for the independent t-test
How would one conduct a Mann-whitney U test
S8
- create a research hypothesis
have an independent groups design - calculate the smallest possible sum of ranks,
- calculate the actual sum of ranks
- subtract the smallest possible sum of ranks from the actual sum of ranks,
- the Mann -w hitney U is the smaller of the two (if you have to variables)
- compare P value to 0.05, accept/reject null, conclusive statement
What is the wilcoxon signed rank test
S8
a Non-parametric alternative for the paired/related test
What is Spearmans Rho
S8
A non-parametric alternative to Pearsons R
Used when the assumptions required for pearson’s r have not been met
What would you have to do in order to conduct a spearmans rho test
s8
- Convert scores to ranks
- Calculate difference in ranks
- Square the difference
- Calculate spearman’s rho using formula
If the ranks are inversly related, what value of Spearmans rho would you get
S8
-1
If the ranks are perfectly related what value of pearsons R would you get
S8
1
What are some limitations of Spearmans Rho
S8
The given formula fails whenever we have tied ranks
What is a 1-variable chi square test used for
S8
Can be used to assess whether observed frequencies in categories are different from what might be expected
Might expect equal distribution or pattern in frequencies
