Chapters 6 & 7

Question 1

Statistical Inference

Answer 1

A procedure by which we use information from a sample to reach conclusions about a population. 2 general areas: Estimation and Hypothesis Testing

Question 2

Estimation

Answer 2

Uses sample data to calculate a statistic.

Question 3

Sampled Population

Answer 3

The population from which you draw your sample

Question 4

Target Population

Answer 4

The population you wish to make an inference about; the population you wish to generalize your results to

Question 5

Point Estimate

Answer 5

A single numerical value used to estimate the corresponding population parameter

Question 6

Interval Estimate

Answer 6

A range of values (with a lower and upper bound) constructed to have a specific probability (or confidence) of including the population parameter

Question 7

Estimator

Answer 7

The rule that tells us how to compute the estimate

Question 8

Estimate

Answer 8

A single computed value

Question 9

Precision of the Estimate (Margin of Error)

Answer 9

Reliability Coefficient times Standard Error

Question 10

Reliability Coefficient

Answer 10

Z or T value when finding CI

Question 11

Probabilistic Interpretation

Answer 11

In repeated sampling of a normal distribution population with a known s.d., 100(1-alpha) percent of all intervals will in the long run include the population mean.

Question 12

Practical Interpretation

Answer 12

When sampling a normally distributed population with a known s.d., we are 100(1-alpha) percent confident that the single computed interval will contain the population mean

Question 13

Z Values for 90, 95, and 99% CIs

Answer 13

90 = 1.645, 95 = 1.96, 99 = 2.58

Question 14

T-Statistic

Answer 14

the result of using s instead of sigma is a distribution with a s.d. > 1, so it is not normal. The resulting distribution is the t-distribution

Question 15

Degrees of Freedom (df)

Answer 15

the number of independent pieces of information that go into the estimate.

Question 16

t vs. z distribution

Answer 16

1. both means = 0, 2. both symmetrical about the mean, 3. both have values from negative to positive infinity, 4. t is more variable than z, 5. The shape of t changes with sample size, when the sample size is infinite the two distributions are identical. 6. t distribution is less peaked in the center and has higher tails.

Question 17

Rule of Thumb for Equal Variance

Answer 17

If the larger sample variance is more than 2x as large as the smaller variance the variances are unequal

Question 18

Hypothesis Testing

Answer 18

Procedure for testing a claim about a population

Question 19

Research Hypothesis

Answer 19

The question or idea that motivates the research

Question 20

Statistical hypothesis

Answer 20

Hypotheses that are stated in such a way that they may be evaluated by statistical techniques

Question 21

1. Data

Answer 21

Determine the type of data and scale of measurement

Question 22

2. Assumptions

Answer 22

Normal Distribution, equal population variances, independence of the samples, random samples, etc

Question 23

3. Hypotheses

Answer 23

Two statistical hypothesis: Ho and Ha

Question 24

Null Hypothesis

Answer 24

Statement of agreement with the conditions presumed true in the population. The complement of the conclusion the researcher is seeking. “The hypothesis of no difference. “ Always a statement of equality.

Question 25

Alternative Hypothesis

Answer 25

What the researcher hopes to conclude. By rejecting Ho you support Ha. States there is a difference.

Question 26

Two-Tailed Hypothesis

Answer 26

Does not specify the direction in which the null is incorrect

Question 27

One-Tailed Hypothesis

Answer 27

Specifies the direction in which the Ho is incorrect

Question 28

4. Test Statistic

Answer 28

A statistic that is computed from the sample statistic. The decision to reject or fail to reject the Ho is based on the magnitude of the test statistic.
(Statistic - hypothesis/standard error)

Question 29

5. Distribution of the Test Statistic

Answer 29

We must determine and specify the probability distribution. ex: the t-distribution with n-1 df. Use z-test if normally distributed and the population variance is known. Use t-test if normally distributed and the population variance is unknown.

Question 30

6. Decision Rule

Answer 30

Find critical values to determine the rejection and non-rejection regions.

Question 31

Level of significance (Alpha)

Answer 31

The probability of rejecting a true null hypothesis. This would be an error, so alpha is typically small (.01, .05 or .10)

Question 32

Type I Error (Alpha)

Answer 32

False positive. When we reject a true null hypothesis. Probability of a type I error is alpha

Question 33

Type II Error (Beta)

Answer 33

False negative. When we fail to reject a false Ho. Beta is not controlled by the investigator. It is effected by sample size, alpha, hypothesized value, and the true value of the parameter. Typically beta > alpha

Question 34

Power

Answer 34

The chance of making a correct decision of rejecting the Ho when the Ho is false. As sample size increases power increases. (1-beta)

Question 35

7. Calculate the Test Statistic

Answer 35

Compare this value to the rejection and non-rejection region

Question 36

8. Statistical Decision

Answer 36

Reject or Fail to Reject Ho

Question 37

9. Conclusion

Answer 37

If the null is rejected, there is evidence in favor of the Ha
If the null is not rejected, there is not evidence in favor of the Ha

Question 38

10. P-values

Answer 38

Tell us the probability associated with obtaining the computed test statistic or more extreme, given that the null hypothesis is true. Smaller values are better for justifying doubting the truth of Ho. If the p-value of the calculated test statistic is less than or equal to alpha, we can conclude the groups are different or there is an association (statistical significance)

Question 39

Statistical Significance

Answer 39

if a p-value is less than or equal to alpha, it implies statistical significance. Ability to state that the observed difference is not due to chance alone. Necessary for clinical significance but does not imply magnitude of effect.