Parametric test assumptions Flashcards by Birwe Leon

Define

Parametric test

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

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Outlier

a data point that differs significantly from other observations

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Linear transformation

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

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Non-parametric test

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

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Central limit theorem

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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Normality

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

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Homogeneity of variance

the assumption that all groups have the same or similar variance

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Independence

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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Residual

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

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Kurtosis

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

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Leptokurtic

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

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Mesokurtic

having the same kurtosis as the normal distribution

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Platykurtic

a statistical distribution in which the excess kurtosis value is negative

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Shapiro Wilkes Test

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

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Q-Q Plot

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

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Univariate outlier

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

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Bivariate outlier

outlier when considering the joint distribution of two variables

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Multivariate outlier

outliers when simultaneously considering multiple variables

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Log transformation

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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Square root transformation

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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Define

Reciprocal transformation

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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Definition

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

Parametric test

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Definition

a data point that differs significantly from other observations

Outlier

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Definition

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

Linear transformation

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# Definition tests don't assume that your data follow a specific distribution

Non-parametric test

# 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

Central limit theorem

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

Normality

# Definition the assumption that all groups have the same or similar variance

Homogeneity of variance

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

Independence

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

Residual

# Definition a measure of the combined weight of a distribution's tails relative to the center of the distribution

Kurtosis

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

Leptokurtic

# Definition having the same kurtosis as the normal distribution

Mesokurtic

# Definition a statistical distribution in which the excess kurtosis value is negative

Platykurtic

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

Shapiro Wilkes Test

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

Q-Q Plot

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

Univariate outlier

# Definition outlier when considering the joint distribution of two variables

Bivariate outlier

# Definition outliers when simultaneously considering multiple variables

Multivariate outlier

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

Log transformation

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

Square root transformation

# 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

Reciprocal transformation

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

**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

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

What is the best central tendency measure for your data? What is your sample size?

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

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

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

*Yi = b₀ + b₁x₁ + b₂x₂ + ei* ## Footnote * Yi =* outcome variable * b₀* = y-intercept * x₁ & x₂ =* predictor variables * b₁ & b₂* = slope of predictors * ei* = error

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

True

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

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.

How can we assess linearity?

* 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

How do you fix when additivity and linearity are voided?

* Apply nonlinear transformation to variables * Add another regressor that is a nonlinear function – polynomial curve * Examine moderators

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

\>30 participants

Is this positively or negatively skewed?

Negative

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

Platykurtic (negative) Mesokurtic (normal distribution) Leptokurtic (positive)

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

Q-Q plot Histogram

What are the two main tests of normality?

Shapiro Wilkes test Q-Q plot

What does a Shapiro Wilkes test do?

* 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)

What does a Q-Q plot do?

What are the three types of outliers?

Univariate Bivariate Multivariate

What type of outlier is this?

Univariate for both variables

What type of outlier is this?

Bivariate

How do you deal with outliers?

* 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)

Why is it a good idea to transform data?

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

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

**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

What are some examples of linear transformations?

Adding a constant to each number, x + 1 Converting raw scores to z-scores, (x – m)/SD Mean centring, x – m

What are some examples of non-linear transformations?

Log, log(x) or ln(x) Square root, 𝑋 Reciprocal, 1/x