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2020 Research Methods > L4 - Nonparametrics > Flashcards

L4 - Nonparametrics Flashcards

1
Q

When we compare means, what type of data do we use?

A

Metric data (numeric)

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2
Q

What is a parametric test?

A

Parametric tests assume a normal distribution of values, or a “bell-shaped curve.”

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3
Q

What is a non-parametric test?

A

A non parametric test (sometimes called a distribution free test) does not assume anything about the underlying distribution

(for example, that the data comes from a normal distribution).

It usually means that you know the population data does not have a normal distribution.

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4
Q

“Analysing the difference between indigenous and non-indigenous smokers”

What type of data is this?

A

Categorical

How many people are using services, how many people do “x”.

Count type data - difference between two categories

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5
Q

What is a binomial test useful for?

A

Useful for tests with binary outcomes

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6
Q

What is a “proportion difference test”?

A

T-tests for proportions.

E.g. are men more likely to smoke than women

Are men more likely to report abuse than women etc

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7
Q

What is a “t-test”?

A

A statistical test to see whether there is a significant difference between two means.

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8
Q

What do non-parametric tests for related samples analyse (e.g. McNemar’s test and Cochran’s Q)?

A

Whether the probability of a binary outcome changes over time

e.g. pass or fail test; 40% fail on first try; only 20% fail on second try

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9
Q

What is a chi-square test used for?

A

A chi-square test is used to determine whether there is a statistically significant difference between the expected frequencies and the observed frequencies in one or more categories of a contingency table.

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10
Q

What are the two types of chi-square tests?

A
  1. Goodness of fit test (or one-way test - 1 independent variable)
  2. Contingency table/cross-tab (or two way analysis - 2 independent variables)
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11
Q

What does a ‘Goodness of Fit Test’ analyse?

A

Tests whether how well an observed distribution of scores matches a distribution expected by chance

Why it’s called a “goodness of fit test” - how good does the IV fit the distribution expected by chance

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12
Q

How many IV’s does a goodness of fit test have?

A

1

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13
Q

What does a distribution expected by chance look like (in a bar-graph)?

A

A rectangle

each variable is the same

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14
Q

Which test would you use to test - “8 starting gates on a race-track: are there more wins in some starting gates?”

Why?

A

Goodness of fit test.

There is only one IV (starting gates) and you are looking to see if there is any difference from chance.

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15
Q

If you observe three vending machines, and you observe 120 people. If based on chance, how many people would use one of those vending machines?

A

40

120/3 = 40

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16
Q

Explain the “chi-squared calculation” χ2 = Σ ( O – E )2 / E

A

Sum of [observed - expected frequency per level]; square the differences; and divide by the expected frequency. This is the Chi-Squared value χ2

χ2 = Σ ( O – E )2 / E

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17
Q

How do you know if a “chi-squared calculation” (χ2) is significant?

A

It must be greater than the critical value

If your value is greater than the critical value, it is significant

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18
Q

What is the critical value based on?

A
  1. The probability level you want to test at
  2. Degrees of freedom
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19
Q

In a goodness of fit test, what is degrees of freedom?

A

The number of levels (variables) minus 1

Df if 3 variables = 3-1 = 2

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20
Q

If the chi-squared calculation in a “goodness of fit test” is greater than the critical value, how would we interpret the results?

A

The observed distribution of scores differs significantly from what would be expected by chance.

E.g. some lanes are used disproportionately more than others in a way that differs from chance

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21
Q

What does a 2-way chi-squared test look at?

A

This is the ‘familiar test’ where one tries to determine whether there is an ASSOCIATION between 2 categorical /ordinal variables

It is a test of independence.

Are the variables independent (no effect) or interdependent (related/ an effect)

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22
Q

A 2-way chi-squared test is trying to determine if two variables are _____ or _____ of one another.

A

Independent (no effect on each other) or Interdependent (related to each other)

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23
Q

What test would we use to determine; “Is the person’s SES and ethnic group related?”

A

2-way chi-squared test

Is SES and ethnic groups independent or interdependent variables?

Other examples - “are smokers more likely to be drinkers” etc.

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24
Q

What is the 2-way chi-squared test formula?

A

[Row-total / Total N] * Column total

E.g. for Mach 1; [row total (180) - grand total (290)] times Mach 1 column total (90)

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25
How is **degrees of freedom** calculated for a **2-way chi-squared test**?
Df = (rows – 1)\*(columns - 1) *For above example; 2 rows minus 1 = 1; 3 columns minus 1 = 2; 1\*2 = Df = 2*
26
When is a **2-way chi-square test** significant?
If it is greater than the **critical value**
27
What does it mean if a **2-way chi-squared test** is significant when interpreting results?
The two variables are **NOT independent** They are **interdependent**
28
One assumption of a chi-squared test is **minimum expected frequency** What % of cells can have a **minimum expected frequency (MEF)** of less than 5 in a **2-way chi-squared test**?
No more than 25% of cells MEF = number of values in a category
29
What test should you use instead of a **2-way chi-squared test** if **minimum expected frequency (MEF)** is violated?
Kolmogorov-Smirnov test
30
For a **2-way chi-squared test** what is the effect size statistic?
Kramer’s V
31
How do you determine the **source of effect** in a 2-way chi-squared test?
Inspection of **standardised residuals** Source of effect can be discerned by comparing expected vs. observed frequencies in cells (**standardised residuals**). Values of 2+ are large
32
χ2(df= 2, N = 50) = 18.69, p \< .01. Is an example APA format of what type of test? How would you write it up if it was a choice between genders and machines (1-3)?
2-way chi-squared test "There was a significant association between gender and choice of machine" "A greater proportion of females preferred machine 1, whereas males preferred machine 3"
33
In a chi-squared test, what is the **standardised residual?** What is it's formula?
A **standardised** score representing the residual leftovers. It is used to see which variable has the most effect. **Formula for standardised residual = O - E / √E**
34
How are **standardised residuals** interpreted?
The standardized residual can be interpreted as any standard score. The mean of the standardized residual is 0 and the standard deviation is 1. ***Anything 2+ is high.*** *Standardized residuals are calculated for each cell in the design.*
35
Why are **standard residuals** helpful for understanding the results of a chi-square?
They are useful in helping to interpret chi-square tables by providing information about **which cells contribute to a significant chi-square**. *Higher scores contribute more to a significant chi-square*
36
What is a **Kappa Test** used for?
To examine **inter-rater reliability** in situations involving 2 independent raters
37
What test would you use to determine: “2 clinical psychologists are asked to assess 50 clients as having or not having clinical depression”. Why?
**Kappa test** *Examining the inter-rater reliability involving 2 independent raters*
38
How do you calculate **Kappa** values?
K = [Po – Pe] / 1 – Pe Where Po = Proportion of cases where there is agreement Pe = Proportion of cases expected to agree by chance Calculations are similar to chi-sq *In week 4 handout*
39
What is a good and very good Kappa value (**K**)?
.5 = good .7 = very good .3 = fair - anything lower is bad
40
When does K (Kappa) tend to be unreliable?
If the base-rate for a phenomenon is very high or very low in the population E.g. \<5% or \>95% in the population of interest I.e If the vast majority are yes or no
41
When is a **Fisher Exact Test** used?
Used when chi-squared test is invalid due to violation of MEF assumption *When you have very small samples*
42
How is a **fisher exact test** interpreted if the results are significant?
Same as a 2-way chi-square test. The two variables are **NOT** **independent** They are **interdependent**
43
What are **binomial tests** used for?
Binomial tests are used to test for the probability of **binary outcomes** e.g., proportion of L vs. R turns, good vs. bad in a batch, clinical vs. non-clinical cases, left vs right-handers
44
What is a **binomial test** attempting to figure out?
Does the probability obtained for one event (e.g., Right) differ from what is expected by chance?
45
What is the most common **binomial test**?
The **Z-test** Or **z-approximation** to binomial
46
What is a **z-test.**
Z-test, tests the **means of 2 population distributions** are different, when **we already know the population variance.** *Must have sample size (N \> 30)* A statistical test that assumes a normal distribution for the null hypothesis.
47
What is the formula for a **z-test**?
**Z = X – Mean / SE** X = observations of binary outcome M (mean) = Number expected by chance SE = standard error = √n.p.(1-p), where p = probability of the event N = number of tests Observed count (number of observations) Expected or Mean = number \* probability In given no other information = .5 (person equally likely to turn left or right) 100 people, Mean = 100 x .5 = 50
48
What test would you use to determine if people tend to ignore a stop sign?
Binomial 2 answers - ignores or stops (50-50)
49
What test would you use to determine if “drug use is increasing in the office”? Is it significant?
Binomal An increase of 5% from 5-10% is therefore significant
50
What is a **proportion difference (PD) test**?
A parametric test that examines whether two samples are drawn from **populations with the same proportions of a given characteristic** i. e. It tests the hypothesis that 2 sample proportions are, or are not, drawn from the same population. * Similar to a t-test (t-test for proportions)* * One of the most important and useful tests*
51
What test should you use to calculate whether “males are more likely to smoke than females” or “are port supporters likely to drive Fords than Crows supporters”?
**Proportion difference test** Looking to see whether the distribution of proportions for the DV of the two different populations are different
52
Why should you use a **proportion difference test** instead of a **chi-squared test**?
**Easier to interpret** (you get a Z score and a test statistic) Difference between proportions is clear Can calculate a **confidence interval**
53
How do you calculate a **proportion difference test**?
P' = the overall probability of the event or quality (e.g., smoking in the whole sample) If E1 = instances in sample 1 (n1) and; E2 = instances in sample 2 (n2) Then p' = [E1+E2] / [n1 + n2]
54
When can a **proportion difference test** be used?
It can be used instead of the non-parametric tests described above when the sample size is sufficient. *Usually when the two sample sizes n1 and n2, are such that n1 or n2.p, or n1 or n2.(1-p) are all \> 5.*
55
Using this **proportion difference test** data. Calculate the Z-value to see whether the difference in values is significant How would you interpret/report the results?
To report this you would say “there was a significant difference in smoking between males and females.
56
How would you measure **repeated non-parametric tests**?
Use a **Cochran’s Q** to measure whether there is a difference across time, and then a **McNemar test** to test differences between specific time points
57
What does a **McNemar test** examine?
Examines whether the probability of a given event is more or less likely in the same sample over time
58
When would you use a **McNemar Test**?
If you have **two related samples** with repeated measures in categorical data analysis
59
What does **Cochran’s Q** measure?
Is the probability of an event less likely in the same sample of people when assessed at a different point in time or in relation to a different choice
60
What values do both a **McNemar test** and a **Cochran’s Q** give you?
A test statistic and associated probability value
61
How would you measure (what tests) whether clients using a CBT program get better over time?
You would use a **Cochran’s Q** to measure whether there is a **difference across time** when using CBT. Then you would use the **McNemar test** to **compare individual time points** (see which time points are most significant)
62
Why wouldn’t you use a **chi-squared test** for measuring whether clients using a CBT program get better over time?
1. Can’t do a Time x Outcome chi-squared test because the data are measured at **different points in time** 2. The data are non-independent (a fundamental assumption of chi-squared test) as they are **collected from the same people**
63
If results for running a repeated measure non-parametric test using Cochran’s and McNemar test are significant. How would you interpret the results?
64
What is a **unstandardised residual**? What is it's formula?
In a 2-way chi-square test; the **standardised residual** is the simple difference of the observed and expected values **Unstandardized residual = O - E**

2020 Research Methods (9 decks)

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