t-Tests & Chi-squared

Question 1

Define:

Variance

Answer 1

The standard deviation squared (σ²).

Much like σ, the variance gives an indication of the extent of spread in the data from the mean.

Question 2

Define:

Standard Deviation (σ)

Answer 2

A measure of spread in the data-points relative to the mean.

Note: There is a difference between population std. deviations and sample std. deviations.

Question 3

Define:

Standard Error

Answer 3

A measure of confidance in the accuracy of the sample mean reflecting the true population mean.

Textbook Definition: The standard deviation of the sampling distribution.

It represents the range of values either side of the sample mean that the population mean value could fall within.

Question 4

What does a small standard error imply?

Answer 4

A higher confidence in the accuracy of the sample mean.

(For representing the population mean).

Question 5

A large standard error implies…

Answer 5

…a lower confidence in the accuracy of the sample mean.

(For representing the population mean).

Question 6

True or False:

A higher standard deviation means a higher standard error.

Answer 6

True

Question 7

Fill-in-the-Blank:

Standard error ____ as the sample size increases.

Answer 7

decreases

Larger sample sizes lead to more clustering of data points around the mean (i.e. central limit theorem and increasing normality of distribution in larger samples).

The standard error gives a confidence interval (range of values) in which the true population mean may lie.

Question 8

What is the formula for a 95% Confidence Interval using the standard error?

Answer 8

SE x 1.96

The error bars then are the mean +/- 1.96SE.

Question 9

What do t-tests assess in relation to variance?

Answer 9

The extent of overlap between the variance aroundtwo group means.

An ANOVA test assesses this too, but with 3+ groups.

Question 10

Fill-in-the-Blank:

A t-test assesses the relationship between a ____ variable and a ____ (____) variable.

Answer 10

1. categorical
2. continuous (numerical)

(e.g. gender and height).

Question 11

List:

The THREE assumptions of a t-test.

Answer 11

1. Each measurement of the sample is independent.
2. Variables are normally distributed.
3. Relatively equal variance between the two groups.

Question 12

What is meant by independence of sample measurements?

Answer 12

Each data point’s value does not affect the measurement of others.

i.e. they are not reliant on each other.

Question 13

In which order should you read the THREE Jamovi outputs for an independent samples t-test?

Answer 13

1. Descriptive statistics.
2. Levene’s Test.
3. Student’s t-test.

The student’s t-test contains information on the p-value, and is used when writing a results section.

(i.e. t(df) = [t-test statistic] , p-value )

Question 14

What does the Levene’s test measure?

Answer 14

A comparison of the group variances.

The p-value generated addresses H₀: ‘the group variances are equal’ / ‘there is no difference in the group variances’.

If the p-value is non-significant, we can say the assumption of equal variances has been met.

Question 15

What FIVE numerical values are included in the descriptive statistics output for a t-test?

Answer 15

1. Population (N)
2. Mean (x)
3. Median (M)
4. Standard Deviation (SD)
5. Standard Error (SE)

Question 16

Define:

Cohen’s d

Answer 16

The number of standard deviations between the group means.

(i.e. the difference between/effect size for the comparison of two means).

This is interpreted in relation to real world contexts.

Question 17

What value is considered small for a Cohen’s d?

Answer 17

.2

Note: This is an approximate guideline.

Question 18

What value is considered medium for a Cohen’s d?

Answer 18

.5

Note: This is an approximate guideline.

Question 19

What value is considered large for a Cohen’s d?

Answer 19

.8

Note: This is an approximate guideline.

Question 20

Fill-in-the-Blank:

A smaller Cohen’s d leads to ____ ____ between the two group distributions.

Answer 20

more overlap

Cohen’s d measure the standard difference between the two group means.

And so, assuming normal distribution, the closer the two means, the more their values will overlap.

Question 21

If the assumption of equal variances is violated in a t-test, what should you do?

Answer 21

Tick the box for Welch’s test (in Jamovi).

A Welch’s t-test is used for comparing the means of two groups with unequal variances.

Question 22

What kind of variables should you use when conducting a chi-squared test?

Answer 22

Two categorical variables.

(e.g. “are females more likely to be religous than males?”)

Question 23

I have two categorical variables. If I want to test for a relationship between them, I should conduct…

Answer 23

A chi-squared test.

Question 24

What does a chi-squared test identify?

Answer 24

Whether or not proportions or percentages across groups are statistically significant.

(e.g. is the fact that, in our sample, 64% of women were religious whilst 44% of men were religious statistically significant?)

Question 25

State:

One limitation of a chi-squared test.

Answer 25

It will tell you if there is a statistically significant difference between groups, but not which one is more or less.

Question 26

True or False:

You CANNOT have more than two levels for each variable in a chi-squared test.

Answer 26

False.

For example, if you were to compare gender and political stance, you might want to have left-wing, centre, and right-wing as levels for the second variable.

However, you will need to select two at a time to compare and see if there is a difference.

Question 27

List:

The TWO assumptions of a chi-squared test:

Answer 27

1. At least 5 measurements in each cell.
2. Independence of data measurements.