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Flashcards in Statistical inference For Two Samples Deck (52)
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1

What is a control?

A treatment meant to serve as a baseline with which the experimental group is compared.

2

What is a placebo?

A control treatment that is fake (e.g. taking a sugar pill) but otherwise indistinguishable from the treatment in the experimental group.

3

What does randomisation of subjects do?

Forms groups that should be similar in all respects before the treatments are applied.

4

What is a matched-pairs design?

Where subjects are matched in pairs, and each treatment is given to one subject in each pair

5

What are three ways in which pairing can occur?

When subjects in one group are ‘matched’ with a similar subject in the other group.

When subjects serve as their own control by receiving both treatments

When, in ‘before and after’ studies, the same subjects are measured twice.

6

What samples do we have in a matched pairs procedure?

Two samples that are dependent.

7

Are there any requirements for the population in a matched-pair procedure?

Yes. The population of resulting differences must be normal (or n>30).

8

What is a matched-pairs procedure also known as?

A paired t-test

9

How does a paired t-test reduce to a one-sample t-test?

By taking the differences in the pairs

10

What is the formula for the test statistic in a matched pairs procedure?

t=(x̅d-0)/(sd/√n)

11

What distribution does the test statistic in a matched-pairs procedure follow?

The t distribution with n-1 degrees of freedom

12

What is the formula for the confidence interval in a matched pairs procedure?

d±(ta/2(sd/√n))

13

What does the critical value come from in the confidence interval for matched pairs?

The t distribution with n-1 degrees of freedom

14

What is the goal of a matched pairs procedure?

To compare the responses to treatments of characteristics of two populations

15

What are 3 conditions of matched pairs procedures?

There are two random samples from distinct populations

The samples are independent

Both populations are normally distributed

16

When are samples independent?

When the subjects are randomly divided into two groups and each group is exposed to a different treatment.

17

What are three criteria for samples to be considered independent?

There is no matching of the subjects in the two samples

The two samples may be of different sizes

Responses in each group are independent of those in the other group.

18

What is the formula for the confidence interval for the difference in population means μ12?

(x̅1-x̅2)±ta/2(√((s12/n1)+(s22/n2)))

19

What is a conservative approximation?

The t‐distribution with degrees of freedom equal to the smaller of n1-1 and n2-1

20

What is a conservative approximation used for?

The confidence interval for the difference in population means μ12

21

For same-subject designs, how is the comparison of treatments done?

Within a subject, thus eliminating differences between subjects from the comparison

22

For different-subjects designs, what does the random variation include?

Subject differences, which is likely to be larger than differences within the same subject

23

How do we make many comparisons at once with an overall measure of confidence in all our conclusions?

Usually in two steps:

Step 1 is an overall test if there is good evidence of any differences among the parameters we want to compare.

Step 2 is a detailed follow-up analysis to decide which of the parameters differ and to estimate how large the differences are.

24

What can't we do when making many comparisons at once with an overall measure of confidence in all our conclusions?

We can’t simply compare two parameters at a time.

25

What does ANOVA stand for?

The ANalysis Of VAriance

26

What null hypothesis is tested in ANOVA?

The null hypothesis that there are no differences in mean response among groups H0123... etc. Therefore all population means are equal

27

What is the alternative hypothesis in ANOVA?

H1: Not all population means are equal

28

What is the formula for a one-way ANOVA test statistic?

Fk-1, N-k=variation among the sample means/variation among individuals in the same sample

29

What variable is given to the number of population means in ANOVA?

k

30

How can we tell if the null hypothesis that all k population means are equal is true?

If the null hypothesis that all k population means are equal is true, the ANOVA  F statistic has the F distribution with k – 1 degrees of freedom in the numerator and N – k degrees of freedom in the denominator