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STAT PSY3062 > Parametric test assumptions > Flashcards

Parametric test assumptions Flashcards

1
Q

Define

Parametric test

A

tests that make assumptions about the parameters of the population distribution from which the sample is drawn

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2
Q

Define

Outlier

A

a data point that differs significantly from other observations

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3
Q

Define

Linear transformation

A

a function from one vector space to another that respects the underlying (linear) structure of each vector space

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4
Q

Define

Non-parametric test

A

tests don’t assume that your data follow a specific distribution

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5
Q

Define

Central limit theorem

A

states that if you have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement , then the distribution of the sample means will be approximately normally distributed

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6
Q

Define

Normality

A

the sampling distribution of the mean is normal or that the distribution of means across samples is normal

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7
Q

Define

Homogeneity of variance

A

the assumption that all groups have the same or similar variance

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8
Q

Define

Independence

A

means that your data isn’t connected in any way (at least, in ways that you haven’t accounted for in your model)

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9
Q

Define

Residual

A

The difference between the observed value of the dependent variable (y) and the predicted value (ŷ)

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10
Q

Define

Kurtosis

A

a measure of the combined weight of a distribution’s tails relative to the center of the distribution

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11
Q

Define

Leptokurtic

A

having greater kurtosis than the normal distribution; more concentrated about the mean

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12
Q

Define

Mesokurtic

A

having the same kurtosis as the normal distribution

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13
Q

Define

Platykurtic

A

a statistical distribution in which the excess kurtosis value is negative

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14
Q

Define

Shapiro Wilkes Test

A

a test that examines if a variable is normally distributed in a population

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15
Q

Define

Q-Q Plot

A

a scatterplot created by plotting two sets of quantiles against one another

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16
Q

Define

Univariate outlier

A

outlier when considering only the distribution of the variable it belongs to

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17
Q

Define

Bivariate outlier

A

outlier when considering the joint distribution of two variables

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18
Q

Define

Multivariate outlier

A

outliers when simultaneously considering multiple variables

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19
Q

Define

Log transformation

A

A type of transformation that can be used to reduce positive skew and stabilise variance and is only defined for positive values > 0

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20
Q

Define

Square root transformation

A

A type of transformation that can be used to reduce positive skew and stabilise variance. It is defined for zero and positive values

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21
Q

Define

Reciprocal transformation

A

A type of transformation that can reduce the impact of large scores and stabilize variance. Transformation reverses the scores, but can be avoided by reversing the scores before transforming

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22
Q

Definition

tests that make assumptions about the parameters of the population distribution from which the sample is drawn

A

Parametric test

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23
Q

Definition

a data point that differs significantly from other observations

A

Outlier

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24
Q

Definition

a function from one vector space to another that respects the underlying (linear) structure of each vector space

A

Linear transformation

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25
Q

Definition

tests don’t assume that your data follow a specific distribution

A

Non-parametric test

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26
Q

Definition

states that if you have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement , then the distribution of the sample means will be approximately normally distributed

A

Central limit theorem

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27
Q

Definition

the sampling distribution of the mean is normal or that the distribution of means across samples is normal

A

Normality

28
Q

Definition

the assumption that all groups have the same or similar variance

A

Homogeneity of variance

29
Q

Definition

means that your data isn’t connected in any way (at least, in ways that you haven’t accounted for in your model)

A

Independence

30
Q

Definition

The difference between the observed value of the dependent variable (y) and the predicted value (ŷ)

A

Residual

31
Q

Definition

a measure of the combined weight of a distribution’s tails relative to the center of the distribution

A

Kurtosis

32
Q

Definition

having greater kurtosis than the normal distribution; more concentrated about the mean

A

Leptokurtic

33
Q

Definition

having the same kurtosis as the normal distribution

A

Mesokurtic

34
Q

Definition

a statistical distribution in which the excess kurtosis value is negative

A

Platykurtic

35
Q

Definition

a test that examines if a variable is normally distributed in a population

A

Shapiro Wilkes Test

36
Q

Definition

a scatterplot created by plotting two sets of quantiles against one another

A

Q-Q Plot

37
Q

Definition

outlier when considering only the distribution of the variable it belongs to

A

Univariate outlier

38
Q

Definition

outlier when considering the joint distribution of two variables

A

Bivariate outlier

39
Q

Definition

outliers when simultaneously considering multiple variables

A

Multivariate outlier

40
Q

Definition

A type of transformation that can be used to reduce positive skew and stabilise variance and is only defined for positive values > 0

A

Log transformation

41
Q

Definition

A type of transformation that can be used to reduce positive skew and stabilise variance. It is defined for zero and positive values

A

Square root transformation

42
Q

Definition

A type of transformation that can reduce the impact of large scores and stabilize variance. Transformation reverses the scores, but can be avoided by reversing the scores before transforming

A

Reciprocal transformation

43
Q

What is the difference between parametric and non-parametric tests?

A

Parametric:

  • ​Assess group means
  • Require that your data follow the normal distribution
    • Except for large sample sizes due to central limit theorem
  • Can deal with unequal variances across groups
  • More powerful

Non-parametric:

  • Assess group medians
  • Don’t require that your data follow the normal distribution
  • Can deal with small sample sizes
44
Q

When deciding between a parametric and non-parametric test what questions should you ask yourself?

A

What is the best central tendency measure for your data?

What is your sample size?

45
Q

Parametric tests are based on the normal distribution and have what assumptions?

A
  1. Additivity and linearity
  2. Normality
  3. Homogeneity of variance
  4. Independence
46
Q

What is the standard linear model equation and what do the variables represent?

A

Yi = b0 + b1x1 + b2x2 + ei

  • Yi =* outcome variable
  • b0* = y-intercept
  • x1 & x2 =* predictor variables
  • b1 & b2 * = slope of predictors
  • ei* = error
47
Q

True or False:

In the Standard linear model, the slope of effect of one predictor does not depend on the values of other variables.

A

True

48
Q

What does linear and additive mean about variables x1, x2 and y?

A

Linear and additive data mean that x1 and x2 predict y

The outcome y is an additive combination of the effects of x1 and x2; it looks like y increases as both x1 and x2 increases.

49
Q

How can we assess linearity?

A
  • Plot of observed vs predicted values (symmetrically distributed around diagonal line)
  • Plot of residuals vs predicted values (symmetrically distributed around horizontal line)
    • look out for bow shape to know that you have violated
50
Q

How do you fix when additivity and linearity are voided?

A
  • Apply nonlinear transformation to variables
  • Add another regressor that is a nonlinear function – polynomial curve
  • Examine moderators
51
Q

What is sample size is large enough for the central limit theorem to apply?

A

>30 participants

52
Q

Is this positively or negatively skewed?

A

Negative

53
Q

What are the three types of kurtosis (in order of increasing central value height)?

A

Platykurtic (negative)

Mesokurtic (normal distribution)

Leptokurtic (positive)

54
Q

When assessing normality what graphical displays do we use to check data or residuals?

A

Q-Q plot

Histogram

55
Q

What are the two main tests of normality?

A

Shapiro Wilkes test

Q-Q plot

56
Q

What does a Shapiro Wilkes test do?

A
  • Tests if data differ from normal distribution
  • Statistically significant (p < .05) → data varies significantly from a normal distribution (i.e., normality assumption is violated)
  • Not statistically significant (p > .05) → data does not vary significantly from a normal distribution (i.e., normality assumption is not violated)
57
Q

What does a Q-Q plot do?

A
58
Q

What are the three types of outliers?

A

Univariate

Bivariate

Multivariate

59
Q

What type of outlier is this?

A

Univariate for both variables

60
Q

What type of outlier is this?

A

Bivariate

61
Q

How do you deal with outliers?

A
  • Remove the case or trim the data
  • Transform the data
  • Change the score (known as winsorizing):
    • Change the score to the next highest value plus some small number (e.g., 1, or whatever is appropriate to the scale of the data)
    • Convert the score to that expected for a z-score of +-3.29
    • Convert the score to the mean plus 2 or 3 standard deviations
    • Convert the score to a percentile of the distribution (e.g., 0.5th or 99.5th percentile)
62
Q

Why is it a good idea to transform data?

A
  1. For convenience or ease of interpretation – standardisation, e.g. z scores allow for simpler comparisons
  2. Reducing skewness – help get closer to meeting normality assumption
  3. Equalising spread or improving homogeneity of variance – produce approximately equal spreads
  4. Linearising relationships between variables – to fit non-linear relationships into linear models
  5. Making relationships additive and therefore fulfilling assumptions for certain tests
63
Q

What is the difference between a linear and non-linear transformation?

A

Linear transformations do not change the shape of the distribution. It may change the value of the mean and/or standard deviation, but the shape of the distribution remains unchanged.

Non-linear transformations change the shape of the distribution

64
Q

What are some examples of linear transformations?

A

Adding a constant to each number, x + 1

Converting raw scores to z-scores, (x – m)/SD

Mean centring, x – m

65
Q

What are some examples of non-linear transformations?

A

Log, log(x) or ln(x)

Square root, 𝑋

Reciprocal, 1/x

STAT PSY3062 (9 decks)

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