# Statistics test 2 formulas

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### paired, dependent, within subjects, repeated measures

What are four other names frequently used for a related-samples t-test?

### population standard deviation

What piece of information are we usually lacking that means we have to compute the standard error when testing hypotheses?

### scores are independent

T-statistic assumption: 1)________, 2) sampled population must be normal (for samples of <30).

### sampled population must be normal (for samples of <30)

T-statistic assumption: 1) scores are independent, 2) ________.

### independent samples t-test

Which type of t-test is performed when you have a between subjects design with two completely separate samples?

### related samples t-test (dependent)

Which type of t-test is performed when you have a within-subjects design. That is, when the same subjects measured more than once?

### related samples t-test (dependent)

Which type of t-test would you use: the data come from the same sample?

### independent samples t-test

Which type of t-test would you use: there are two completely separate samples.

### independent samples t-test

Which type of t-test would you use: the data come a study with a between-subjects design.

### related samples t-test (dependent)

Which type of t-test would you use: the data come from a study with a repeated measures design?

### different

Do we apply the independent samples t-test when samples are taken from the same population or different populations?

### independent samples t-test

For which inferential test do you need to calculate pooled variance?

### u1 - u2 = 0

What is the null hypothesis for an independent samples t-test?

### independent samples t-test

Which test statistic do these hypotheses go with?

### degrees of freedom, independent samples t-test

What does this equation test for? Which inferential test does it go with?

### independent samples, related (dependent) samples

What are the two types of t-test?

### standard deviation

A measure representing the average difference between the scores and the mean of a distribution

### variance

The standard deviation of a distribution squared.

### degrees of freedom

Number of scores that can vary in the calculation of a statistic.

### reject

If the observed difference is above what you'd expect by chance, you should ________ the null hypothesis.

### sampling error

Difference between the population mean and sample mean.

### t-test

What inferential statistical test would you do if your research design had one factor with two groups.

### 1-factor ANOVA (f-ratio)

What type of inferential statistical test would you use if your research design had one factor with more than two unrelated groups?

### 1-factor ANOVA

What type of inferential statistical test would you do if your research design had one factor with more than two matched groups?

### f-ratio

What is the test statistic for an ANOVA?

### variance (mean squares)

F is the ratio of ________ between treatments and _______ within treatments

### all groups are equal

What is the null hypothesis of an ANOVA test (in words)?

### planned comparisons and post hoc tests

If you run an ANOVA and reject the null hypothesis, what is done next?

### related samples t-test

What type of t-test is performed when there are repeated measures - within subjects design: a single sample is measured more than once on the same dependent variable?

### related samples t-test

What type of t-test is performed when there are matched subjects: two samples, each individual in one sample is matched one-to-one with an individual in the other sample?

### matched subjects, repeated measures (or within groups)

For which two experimental designs do we use the related samples t-test to analyse?

### related samples t-test

If data were collected in an experiment where participants were measured before and after a treatment, which type of t-test would be conducted (assuming there was only one factor and two levels)?

### related samples t-test

If participants in two groups were matched for their age, gender, education level and marital status, which type of t-test would be conducted (assuming there was only one factor and two levels?)

### related samples t-test

Which type of t-test involves analysing the difference scores between groups?

### related samples t-test

Which t-test has an hypothesis of no difference?

### related samples t-test

Which test statistic do these hypotheses go with?

### related samples t-test, 2, no, 0

What does this equation test for? How many samples have been taken from the population? Is the population standard deviation known? What is the mean differences of the population assumed to be?

### fewer subjects

Advantages of the repeated measures t-test: 1) _________, 2) we can study change over time, 3) reduces individual differences.

### we can study change over time

Advantages of the repeated measures t-test: 1) fewer subjects, 2) _________, 3) reduces individual differences.

### reduces individual differences

Advantages of the repeated measures t-test: 1) fewer subjects, 2) we can study change over time, 3) _________.

### time effects (Participants are measured in 2 conditions at 2 different times)

Problems of the repeated measures t-test: 1) _________, 2) previous treatment effects (in the case of multiple treatments).

### previous treatment effects (in the case of multiple treatments)

Problems of the repeated measures t-test: 1) time effects (Participants are measured in 2 conditions at 2 different times), 2) _________.

### independent observations

Assumptions of the repeated measures t-test: 1) _________, 2) population difference scores are normal (for samples of < 30).

### population difference scores are normal (for samples of < 30)

Assumptions of the repeated measures t-test: 1) independent observations, 2) _________.

### related samples t-test (because the computer has to calculate differences)

In SPSS, for which type of t-test do data from different groups of observations go into separate columns?

### independent samples t-test

In SPSS, for which type of t-test do data from different groups of observations go into the same columns (and labels into the second column)?

### mean difference, related samples t-test

What does this equation test for? Which test statistic does it go with?

### sum of squares, related samples t-test

What does this equation test for? Which test statistic does it go with?

### estimated standard error, related samples t-test

What does this equation test for? Which test statistic does it go with?

### can only be used with two groups (or populations)

What is a major limitation of t-tests?

### can be used with 2 or more populations

What is the advantage of ANOVA tests?

### Independent variable

Which part of an experimental design (or quasi-experimental) is called a "factor" in an ANOVA?

### Levels

What are the conditions or treatments that make up an experiment's independent variable called in an ANOVA?

### ANOVA

Which inferential test do these hypotheses go with?

### more than 2 groups (treatments)

When do you use an ANOVA?

### increased probability of type-1 error

Why not use multiple t-tests if you have more than 2 groups (treatments?)

### chance (individual differences and experimental error)

Differences between treatments in an experiment are due to: 1) _______, 2) treatment effects.

### treatment effects

Differences between treatments are due to: 1) chance (individual differences and experimental error), 2) _______.

### positive

In an F-distribution, the ratios are all ________.

### chance

Differences within treatment are due to _________.

### K

Which variable in the ANOVA formula represent the number of groups or treatment conditions (number of levels of the factor)?

### N

Which variable in the ANOVA formula represents the total number of scores from all treatments (n1 n2 n3 etc.)?

### N

Which variable in the ANOVA formula represents the total number of scores in the entire study?

### T

Which variable in the ANOVA formula represent the sum of scores (ΣX) for each treatment condition (treatment total)?

### G

Which variable in the ANOVA formula represent the sum of all the scores in the study (grand total).

### G

If you sum all the Ts (sum of scores for each treatment), what variable represents the result?

### total sum of squares

Does this formula calculate the total sum of squares or does it calculate the sum of squares between treatments?

### sum of squares between treatments

Does this formula calculate the total sum of squares or does it calculate the sum of squares between treatments?

### sum of squares within treatments

If you add all the sums of squares from each treatment, what does it calculate?

### ratio

F is the ________ of variance between treatments and variance within treatments

### df between, df within

When reading an ANOVA table: df total = ________ + _______

### SS between, SS within

When reading an ANOVA table; SS total = ________ + _______

### mean squares between, mean squares within

When reading an ANOVA table; F = ratio of ________ / _______.

### N-k

Complete the formula using the standard variables. In an ANOVA, df within treatments = _______

### k-1

Complete the formula using the standard variables. In an ANOVA, df between treatments = _______

### N-1

Complete the formula using the standard variables. In an ANOVA, total df =

### mean squares

What measure of variance is used to compare groups in ANOVA calculations?

### sum of squares

What measure of variance is used to compare groups in t-tests?

### F-ratio, single factor ANOVA

What does this formula calculate? Which inferential test is it used in?

### mean squares (variance in an ANOVA calculation)

What does this formula calculate? SS/df

### no

Can an F-ratio be a negative number?

### Yes

Can a t-score be a negative number?

### No

Can variance be a negative number?

### 1

When the null is true (no differences between groups), the F-ratio should be around _____

### True

When the null hypothesis is ________, F-ratio should be around 1 (the two variances will be around the same size).

### 1

Scores in a F distribution pile up around ____.

### between groups

To look up critical values in F distribution table, we need the degrees of freedom of the numerator and the degrees of freedom of the denominator. The degrees of freedom of the numerator is the same as the df of what?

### df within groups

To look up critical values in F distribution table, you need the the degrees of freedom of the numerator and degrees of freedom of the denominator. The degrees of freedom of the denominator is the same as the df of what?

### Reduces type 1 error

Why use an ANOVA over a t-test?

### >

To reject the null hypothesis using an ANOVA, should F-ratio obtained be > or < than the critical F-ratio that you look up in the F-distribution table?

### 2

What is the minimum number of treatments needed to run an ANOVA?

### effort required (t-test is less effort to calculate than ANOVA)

Since an ANOVA can be done when comparing two samples, why do we use an independent samples T-test?

### Tukey's HSD

What is the name of the post hoc test we use if the ANOVA finds that the F-ratio is significant and we can reject the null hypothesis?

### Honestly significant difference

What does the HSD in "Tukey's HSD" post hoc test mean?

### reject the null hypothesis

What are the conditions necessary before we bother running a post hoc test? 1) ________, 2) 3 or more treatment conditions (groups)

### 3 or more treatment conditions (groups)

What are the two conditions necessary before we bother running a post hoc test ? 1) reject the null hypothesis, 2) ________.

### equal sized groups

In addition to conditions that must be met to run a post hoc test after an ANOVA, what additional condition must be met before calculating a Tukey's HSD?

### a look-up table

Where do we get the 'q' variable for Tukey's HSD formula?

### 1

When the null is true (no differences between groups), F should be around _____

### 1

Scores in a F distribution pile up around _____

### df between

When reporting an ANOVA result F (2, 12) = 19.43, p < .05, what does the 2 refer to?

### df within

When reporting an ANOVA result F (2, 12) = 19.43, p < .05, what does the 12 refer to?

### 19.43

What is the f-ratio in the following ANOVA result F (2, 12) = 19.43, p < .05?

### they have the same variance

What does the independent samples t-test assume about the variances of the two samples?

### variance

The independent samples t-test assumes that the two samples have the same ________

### Pearson's r correlation

Which test statistic do these hypotheses go with?

### df between

An APA ANOVA result is presented thus: F (X, 12) = 19.43, p < .05 . What does X represent?

### df within

An APA ANOVA result is presented thus: F (2, X) = 19.43, p < .05 . What does X represent?

### f-ratio

An APA ANOVA result is presented thus: F (2, 12) = X, p < .05 . What does X represent?

Example: