Mathematical Stuff Flashcards by Kylie hinde

You can use factor analysis to find

New constructs amongst your data

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What is exploratory factor analysis used for

To identify underlying structure in a group of variables.

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Put simply in factor analysis we are looking for

Clusters of highly correlated items

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Factor analysis can also be used to establish

Construct validity (sure we’re measuring what we intend to measure)

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Factor analysis seeks out

Relationships between variables

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Factor analysis tries to put a factor where

A group of items are

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1st of Two important types of factor analysis is…

Force all factors to have a correlation of 0 (no overlap btwn factors completely independent)

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We can use a scree plot to interpret

Factor analysis

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Three steps to do research…

Collect data, assess the sample
Check data fits the mathematical assumptions of the statistical model
Test hypothesis - fit model

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How do you determine goodness of fit?

Significance
Power
Effect size

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Sample representativeness is

Is the sample representative of the population? Is there a fit?

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Inferential stats are dependent on

A match between our sample and the pop

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Inferential stats is about

Inferring!!!

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Predicting any outcome comes down to

The model plus a degree of error

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Mean is a hypothetical value as it

Doesn’t have to represent a data point in the sample

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The mean is a

Description of what’s happening in the sample

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We use the mean to

Estimate the value in the population

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How do we assess the for of the model?

See how much each of the data points vary from the model

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Standard deviation tells us

How good our mean fits the data that we’ve captured

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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

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SD only describes

The sample you’ve collected

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What do we use to determine if a sample is a good representation of the population?

Standard error of the mean

Confidence intervals

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Sampling variation is when

Each sample collect has a different mean

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Standard error of the mean is looking at

samples and how spread they are in a distribution of samples

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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

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

1. Measures of central tendency are equal (mean = median = mode) 2. Unimodal (only 1 score that occurs frequently) 3. Skew = 0 4. Kurtosis = 0 5. 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

1. Cohens D 2. Pearson product moment correlation co-efficient (r) 3. 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?

If pearsons r is .10 there is how much variance explained?