Mathematical Stuff Flashcards
You can use factor analysis to find
New constructs amongst your data
What is exploratory factor analysis used for
To identify underlying structure in a group of variables.
Put simply in factor analysis we are looking for
Clusters of highly correlated items
Factor analysis can also be used to establish
Construct validity (sure we’re measuring what we intend to measure)
Factor analysis seeks out
Relationships between variables
Factor analysis tries to put a factor where
A group of items are
1st of Two important types of factor analysis is…
- Force all factors to have a correlation of 0 (no overlap btwn factors completely independent)
We can use a scree plot to interpret
Factor analysis
Three steps to do research…
- Collect data, assess the sample
- Check data fits the mathematical assumptions of the statistical model
- Test hypothesis - fit model
How do you determine goodness of fit?
Significance
Power
Effect size
Sample representativeness is
Is the sample representative of the population? Is there a fit?
Inferential stats are dependent on
A match between our sample and the pop
Inferential stats is about
Inferring!!!
Predicting any outcome comes down to
The model plus a degree of error
Mean is a hypothetical value as it
Doesn’t have to represent a data point in the sample
The mean is a
Description of what’s happening in the sample
We use the mean to
Estimate the value in the population
How do we assess the for of the model?
See how much each of the data points vary from the model
Standard deviation tells us
How good our mean fits the data that we’ve captured
How do we work out the SD
Add up variances of scores to the mean. Sum of squared errors then divide by n -1 (df) convert by square rooting it
SD only describes
The sample you’ve collected
What do we use to determine if a sample is a good representation of the population?
Standard error of the mean
Confidence intervals
Sampling variation is when
Each sample collect has a different mean
Standard error of the mean is looking at
samples and how spread they are in a distribution of samples
Standard error is an estimate based of the
Mean that we already have and the sample size we have
A small standard error indicates
Our sample is likely to be an accurate reflection of the population
Model of observations in sample is where we
Fit the mean/model to the sample using SD
We estimate the SE from the
SD
To calculate the SE you
Take SD divide by square root of n
Confidence intervals mean that the range
Of values within which the population mean actually falls
Conventional confidence intervals are calculated at
95%
What does 95% CI mean?
That 95% of time true value of pop will fall between these limits
Normal distribution has a
Mean of 0 and a SD of 1
For z scores we take
The raw score minus the mean and divide by SD
We use the z score to calculate
Our upper and lower boundaries of the CI
To calculate upper CI interval
M + (z score x SE)
To calculate lower CI interval
M - (z score x SE)
The larger the SE then what happens to the CI boundary
It’s bigger
What happens if we have two samples whose confidence intervals don’t overlap?
They both contain pop mean BUT they come from diff populations!
What could cause two samples to come from diff populations?
Confounding variables
Manipulated in a different way by experimenter
What are the 5 criteria used to judge if data collected is distributed normally
- Measures of central tendency are equal (mean = median = mode)
- Unimodal (only 1 score that occurs frequently)
- Skew = 0
- Kurtosis = 0
- No outliers
Positive skew is
Long right tail
Negative skew has a
Long LEFT tail
We assess the extent of Skewness by
Standardising the skew
To standardise the Skewness we
Divide skew by its standard error
How do you calculate z score???
Score minus the mean divide by SD
To calculate skew you
Skew Score - mean divide by standard error of Skewness (round up)
If it’s a sig problem if Skewness is larger than
1.96 (or 2)
Kurtosis measures the extent to which
Observations cluster around a central point
To calculate kurtosis we take
Divide kurtosis by its standard error
If kurtosis is greater than……….we have sig kurtosis
1.96
Outliers indicate
An error in measurement
Error in data recording
Error in data entry
Legitimate
How do we check for outliers?
Convert all scores to a z score
Outliers will have a z score greater than
+2 or -2
What are two tests that looks for normality?
The kolmogorov-smirnov
The Shapiro-wilk
If you have a smaller sample don’t use
Kolmogorov smirnov
What’s the problem with Shapiro wilk?
Larger sample will often give u sig results! Making type 1 error
Q-Q chart plots can also
Assess normality
What does normality look like on a Q-Q plot test?
A straight diagonal line
Homogeneity of variance refers to
Variances should be the same through the data. Ie scorches hang around the mean. The spread of the data within each of the groups
You use levenes test to get
Homogeneity of variance. Tells us if variances of two groups or more are equal
Levenes has a sig of
> .05
One tailed test is used for
Directional hypothesis
It’s easier to get a sig result if I have ……tailed hypothesis
One
Type 1 error is where we
Reject null and assume sig when no sig
Type 2 error is where we
Retain null and there is sig
Two calculations that are important in sig testing…
Power
Observed power
What is power?
Probability of finding a sig diff in a sample, given a diff between groups of a particular size and specific sample
What is observed power?
Likelihood of finding a sig diff btwn groups in any sample with the same sample size in the study, assuming that the differences btwn groups in the study is the same as the diff btwn groups in the pop
What is acceptable power
.8 or %80
What is effect size?
When any statistical analysis produces a sig value for the relationship being made
The effect size indicates
Diff among group means that can’t be attributed to error
AND
is a relationship btwn two variables that can’t be attributed to error
What are the 3 measures of effect size
- Cohens D
- Pearson product moment correlation co-efficient (r)
- Omega (t-tests and ANOVA)
What is a large effect size
.8 cohens D
.50 pearsons r
.14 omega
What’s a medium effect size
Cohens D .5
Pearsons r .3
Omega .06
What is a small effect size
.20 cohens D
.10 pearsons r
.01 omega
If pearsons r is .50 it explains how much variance there is btwn the IV and the DV?
%25
If pearsons r is .30 it explains how much variance there is?
9%
If pearsons r is .10 there is how much variance explained?
1%
