Mathematical Stuff Flashcards

0
Q

You can use factor analysis to find

A

New constructs amongst your data

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1
Q

What is exploratory factor analysis used for

A

To identify underlying structure in a group of variables.

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2
Q

Put simply in factor analysis we are looking for

A

Clusters of highly correlated items

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3
Q

Factor analysis can also be used to establish

A

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

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4
Q

Factor analysis seeks out

A

Relationships between variables

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5
Q

Factor analysis tries to put a factor where

A

A group of items are

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6
Q

1st of Two important types of factor analysis is…

A
  1. Force all factors to have a correlation of 0 (no overlap btwn factors completely independent)
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7
Q

We can use a scree plot to interpret

A

Factor analysis

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8
Q

Three steps to do research…

A
  1. Collect data, assess the sample
  2. Check data fits the mathematical assumptions of the statistical model
  3. Test hypothesis - fit model
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9
Q

How do you determine goodness of fit?

A

Significance
Power
Effect size

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10
Q

Sample representativeness is

A

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

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11
Q

Inferential stats are dependent on

A

A match between our sample and the pop

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12
Q

Inferential stats is about

A

Inferring!!!

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13
Q

Predicting any outcome comes down to

A

The model plus a degree of error

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14
Q

Mean is a hypothetical value as it

A

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

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15
Q

The mean is a

A

Description of what’s happening in the sample

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16
Q

We use the mean to

A

Estimate the value in the population

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17
Q

How do we assess the for of the model?

A

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

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18
Q

Standard deviation tells us

A

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

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19
Q

How do we work out the SD

A

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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20
Q

SD only describes

A

The sample you’ve collected

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21
Q

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

A

Standard error of the mean

Confidence intervals

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22
Q

Sampling variation is when

A

Each sample collect has a different mean

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23
Q

Standard error of the mean is looking at

A

samples and how spread they are in a distribution of samples

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24
Q

Standard error is an estimate based of the

A

Mean that we already have and the sample size we have

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25
Q

A small standard error indicates

A

Our sample is likely to be an accurate reflection of the population

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26
Q

Model of observations in sample is where we

A

Fit the mean/model to the sample using SD

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27
Q

We estimate the SE from the

A

SD

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28
Q

To calculate the SE you

A

Take SD divide by square root of n

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29
Q

Confidence intervals mean that the range

A

Of values within which the population mean actually falls

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30
Q

Conventional confidence intervals are calculated at

A

95%

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31
Q

What does 95% CI mean?

A

That 95% of time true value of pop will fall between these limits

32
Q

Normal distribution has a

A

Mean of 0 and a SD of 1

33
Q

For z scores we take

A

The raw score minus the mean and divide by SD

34
Q

We use the z score to calculate

A

Our upper and lower boundaries of the CI

35
Q

To calculate upper CI interval

A

M + (z score x SE)

36
Q

To calculate lower CI interval

A

M - (z score x SE)

37
Q

The larger the SE then what happens to the CI boundary

A

It’s bigger

38
Q

What happens if we have two samples whose confidence intervals don’t overlap?

A

They both contain pop mean BUT they come from diff populations!

39
Q

What could cause two samples to come from diff populations?

A

Confounding variables

Manipulated in a different way by experimenter

40
Q

What are the 5 criteria used to judge if data collected is distributed normally

A
  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
41
Q

Positive skew is

A

Long right tail

42
Q

Negative skew has a

A

Long LEFT tail

43
Q

We assess the extent of Skewness by

A

Standardising the skew

44
Q

To standardise the Skewness we

A

Divide skew by its standard error

45
Q

How do you calculate z score???

A

Score minus the mean divide by SD

46
Q

To calculate skew you

A

Skew Score - mean divide by standard error of Skewness (round up)

47
Q

If it’s a sig problem if Skewness is larger than

A

1.96 (or 2)

48
Q

Kurtosis measures the extent to which

A

Observations cluster around a central point

49
Q

To calculate kurtosis we take

A

Divide kurtosis by its standard error

50
Q

If kurtosis is greater than……….we have sig kurtosis

A

1.96

51
Q

Outliers indicate

A

An error in measurement
Error in data recording
Error in data entry
Legitimate

52
Q

How do we check for outliers?

A

Convert all scores to a z score

53
Q

Outliers will have a z score greater than

A

+2 or -2

54
Q

What are two tests that looks for normality?

A

The kolmogorov-smirnov

The Shapiro-wilk

55
Q

If you have a smaller sample don’t use

A

Kolmogorov smirnov

56
Q

What’s the problem with Shapiro wilk?

A

Larger sample will often give u sig results! Making type 1 error

57
Q

Q-Q chart plots can also

A

Assess normality

58
Q

What does normality look like on a Q-Q plot test?

A

A straight diagonal line

59
Q

Homogeneity of variance refers to

A

Variances should be the same through the data. Ie scorches hang around the mean. The spread of the data within each of the groups

60
Q

You use levenes test to get

A

Homogeneity of variance. Tells us if variances of two groups or more are equal

61
Q

Levenes has a sig of

A

> .05

62
Q

One tailed test is used for

A

Directional hypothesis

63
Q

It’s easier to get a sig result if I have ……tailed hypothesis

A

One

64
Q

Type 1 error is where we

A

Reject null and assume sig when no sig

65
Q

Type 2 error is where we

A

Retain null and there is sig

66
Q

Two calculations that are important in sig testing…

A

Power

Observed power

67
Q

What is power?

A

Probability of finding a sig diff in a sample, given a diff between groups of a particular size and specific sample

68
Q

What is observed power?

A

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

69
Q

What is acceptable power

A

.8 or %80

70
Q

What is effect size?

A

When any statistical analysis produces a sig value for the relationship being made

71
Q

The effect size indicates

A

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

72
Q

What are the 3 measures of effect size

A
  1. Cohens D
  2. Pearson product moment correlation co-efficient (r)
  3. Omega (t-tests and ANOVA)
73
Q

What is a large effect size

A

.8 cohens D
.50 pearsons r
.14 omega

74
Q

What’s a medium effect size

A

Cohens D .5
Pearsons r .3
Omega .06

75
Q

What is a small effect size

A

.20 cohens D
.10 pearsons r
.01 omega

76
Q

If pearsons r is .50 it explains how much variance there is btwn the IV and the DV?

A

%25

77
Q

If pearsons r is .30 it explains how much variance there is?

A

9%

78
Q

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

A

1%