Stats Exam #3

Front 1

What is z*

Back 1

Z* - is the number of standard deviations from the mean for a given percent confidence interval. Example 95% is 1.96 (2) standard deviations away from the mean. The whole 95% is captured between –z* and z* standard deviations away from the mean.

Front 2

Margin of Error is calculated by

Back 2

z*(Sigma/Sqrt(n))

Front 3

Confidence Interval is calculated by

Back 3

Xbar +/- z*(Sigma/Sqrt(n))

Front 4

s (standard deviation for a sampling distribution) is calculated by

Back 4

s= (sigma/Sqrt(n))

Front 5

z* for 95% confidence is

Back 5

1.960

Front 6

Null Hypothesis

Back 6

The test is designed to asses the strength of the evidence against the null hypothesis. The statement of "no difference"

Front 7

Alternative Hypothesis

Back 7

The about the population we are trying to find evidence for.

Front 8

A small p-value means

Back 8

strong evidence against Ho provided by the data.

Front 9

large p value means

Back 9

fail to give evidence against Ho.

Front 10

Level of Significance

Back 10

Alpha, usually .01 and .05

Front 11

Statistically significant happens when

Back 11

P < alpha. When results are statistically significant we have evidence to reject Ho.

Front 12

Test Statistic

Back 12

A statistic on which a statistical test is based, used to accept or refute the null hypothesis. Z and T

Front 13

a smaller z* is the same as a

Back 13

lower confidence level (Smaller % of confidence)

Front 14

because n appears under a square root sign, we must take four times as many observations in order to cut the margin of error in half.

Back 14

=

Front 15

How do you find standard error

Back 15

s/sqrt(n)

Front 16

What is standard of error

Back 16

it is the same as a standard deviation for a sample mean distribution. but for a population where sigma is unknown.

Front 17

Level of Significance

Back 17

Alpha

Front 18

The probability of failing to reject a false null hypothesis

Back 18

Beta

Front 19

The hypothesis that the researcher wants to prove or verify; a statement about the value of a parameter that is either “less than,” “greater than,” or “not equal to.”

Back 19

Alternative hypothesis:

Front 20

A test for comparing the means of two independent samples or two treatments where the test statistics has an approximate t distribution.

Back 20

Approximate two-sample t test:

Front 21

A statistical procedure for testing the equality of means using variances.

Back 21

ANOVA (Analysis of Variance

Front 22

When sampling from a non-Normal population, the sampling distribution of x¯ is approximately Normal whenever the sample is large and random.

Back 22

Central Limit Theorem

Front 23

The value of the parameter given in the null hypothesis. E.g. µ0 is a claimed parameter value.

Back 23

Claimed parameter value

Front 24

The basic premises for inferential procedures. If the conditions are not met, the results may not be valid.

Back 24

Conditions

Front 25

Normality of the original population & SRS. (Note: We can use a t-distribution procedure when n < 40 provided the data have no outliers. We must have an SRS, however.) Check (1) data collection and (2) if n < 40, check the outliers in data plot; if n ≥ 40, apply CLT.

Back 25

Conditions necessary for a one-sample t procedure (using t* for C.I. or getting P-value from t table):

Front 26

Conditions necessary for a two-sample t procedure (using t* for C.I. or getting P-value for t table)

Back 26

Normality of both populations & either stratified sample (independent SRS’s) or random allocation. Check (1) data collection and (2) if n1 + n2 < 40, check for outliers in both data plots; if n1 + n2 ≥ 40, apply CLT.

Front 27

Conditions necessary for ANOVA

Back 27

Normality of all populations, equality of variances & either stratified random sample (independent SRS’s) or random allocation. Check (1) data collection, (2) if n1 + n2 +…+ nk < 40, check for outliers in all k data plots; if n1 + n2 + … nk ≥ 40, apply CLT, and (3) largest standard deviation divided by smallest standard deviation < 2.

Front 28

An estimate of the value of a parameter in interval form with an associated level of confidence; in other words, a list of reasonable or plausible values for the parameter based on the value of a statistic. E.g. a confidence interval for µ gives a list of possible values that µ could be based on the sample mean.

Back 28

Confidence interval

Front 29

: A test for comparing the means from two independent samples or two treatments where the degrees of freedom are taken to be the minimum of (n1-1) and (n2-1).

Back 29

Conservative two-sample t test

Front 30

What happens to the width of a confidence interval when sample size is increased (or level of confidence is decreased.)

Back 30

Decreased

Front 31

A characteristic of the t-distribution (e.g. n – 1 for a one-sample t); a measure of the amount of information available for estimating σ using s.

Back 31

Degrees of freedom

Front 32

A condition for ANOVA; the condition is met when the largest standard deviation divided by the smallest standard deviation is less than 2

Back 32

Equal Variance

Front 33

The appropriate statistical conclusion when the P-value is greater than α

Back 33

Fail to reject H0

Front 34

Results from statistical analyses performed on non-random samples or experimental data obtained without random allocation of treatments to individuals

Back 34

Garbage

Front 35

Using results about sample statistics to draw conclusions about population parameters.

Back 35

Inference

Front 36

The basis for hypothesis testing and confidence interval estimation.

Back 36

Laws of probability

Front 37

Level of confidence

Back 37

The percent of the time that the confidence interval estimation procedure will give you intervals containing the value of the parameter being estimated. (Note: This can only be defined in terms of probability as follows: “The probability that the confidence interval to be computed (before data are gathered) will contain the value of the parameter.” After data are collected, level of confidence is no longer a probability because a calculated confidence interval either contains the value of the parameter or it doesn’t.)

Front 38

The probability of rejecting a true null hypothesis; equivalently, the largest risk a researcher is willing to take of rejecting a true null hypothesis.

Back 38

Level of significance (symbolized by α)

Front 39

A test with “<” in the alternative hypothesis. This is a one-sided test.

Back 39

Lower-tailed test (Also called a left-tailed test)

Front 40

: The maximum amount that a statistic value will differ from the parameter value for the middle 95% of the distribution of all possible statistics. (Note: 95% can be changed to any other level of confidence.)

Back 40

Margin of error for 95% confidence

Front 41

Either two measurements are taken on each individual such as pre and post OR two individuals are matched by a third variable (different from the explanatory variable and the response variable) such as identical twins.

Back 41

Matched pairs

Front 42

Matched pairs t test

Back 42

The hypothesis testing method for matched pairs data. The typical null hypothesis is H0:µd = 0 where µd is the mean difference between treatments. For this test, a difference is computed within every pair. The mean and standard deviation of these differences are computed and used in computing the test statistics.
μ0: The claimed value of the population mean given in H0.

Front 43

μ0

Back 43

The claimed value of the population mean given in H0.

Front 44

Multiple Analyses

Back 44

Performing two or more tests of significance on the same data set. This inflates the overall α (probability of making a type I error) for the tests. (The more analyses performed, the greater the chances of falsely rejecting at least one true null hypothesis.)

Front 45

Null hypothesis

Back 45

The hypothesis of no difference or no change. The hypothesis that the researcher assumes to be true until sample results indicate otherwise. Generally, the hypothesis that the researcher wants to disprove. (Note: Interpretations of P-value and statistically significant need to say something about “if H0 is true” in order to be correct.)

Front 46

: The difference between the observed statistic and the claimed parameter value; e.g. – μ0.

Back 46

Observed effect

Front 47

A test where the alternative hypothesis contains either “<” or “>”

Back 47

One-sided or one-tailed test

Front 48

An inferential statistical procedure that uses the mean for one sample of data for either estimating the mean of the population or testing whether the mean of the population equals some claimed value.

Back 48

One-sample t test

Front 49

: An observation that falls outside the pattern of the data set. For one sample of data, an outlier will be any observation that is a long way from the rest of the data

Back 49

Outlier

Front 50

: A characteristic of a population that is usually unknown; this characteristic could be the mean (μ), median, proportion, standard deviation (σ), etc.

Back 50

Parameter

Front 51

: The probability of rejecting a false null hypothesis; computed as 1 – β. Increase power by increasing sample size or increasing α

Back 51

Power:

Front 52

Practical significance

Back 52

A difference between the observed statistic and the claimed parameter value that is large enough to be worth reporting. To assess practical significance, look at the numerator of the test statistic and ask ‘Is it worth anything?’ If yes, then results are also of practical significance. Note: Do not assess practical significance unless results are statistically significant

Front 53

P-value

Back 53

The probability of getting a test statistic as extreme or more extreme than the value observed assuming H0 is true. OR The probability of obtaining a test statistic value as far or farther from the value actually obtained if H0 were true

Front 54

The appropriate statistical conclusion when P-value < α.

Back 54

Reject H0

Front 55

The variability of sample results from one sample to the next—something we must measure in order to effectively do inference. Margin of error only covers sampling variability

Back 55

Sampling variability

Front 56

Significance lever (α)

Back 56

Level of Significance

Front 57

A measure of the variability (spread) of data in a sample about

Back 57

Standard deviation (s

Front 58

A measure of the variability of the sampling distribution of xbar ; equals σ / sqrt(n) .

Back 58

Standard deviation of xbar

Front 59

: A measure of the variability of the sampling distribution of xbar; estimates the standard deviation of the sampling distribution of xbar ; computed using the formula: s / sqrt(n) .

Back 59

Standard error of xbar

Front 60

Standard of a statistic

Back 60

An estimate of the standard deviation of the sampling distribution of the statistic; in other words, it is a measure of the variability of the statistic. Note: The denominators of most test statistics are called standard errors.

Front 61

A characteristic of a sample; a number computed from sample data (without any knowledge of the value of a parameter) used to estimate the value of a parameter. Examples include , the sample mean, and s, the sample standard deviation

Back 61

Statistic

Front 62

: A difference between the observed statistic and the claimed parameter value as given in H0 that is too large to be due to chance. (An observed effect that is too large to be due to chance.) Results are significant when P-value < α. Just because the results are statistically significant does not imply that the results are important.

Back 62

Statistical significance

Front 63

Results of a study that differ too much from what we expected because of randomization to attribute to chance variation

Back 63

Statistically significant

Front 64

: A distribution specified by degrees of freedom used to model test statistics for the one-sample t test, the two-sample t test, etc. where σ (‘s) is (are) unknown. Also used to obtain a confidence interval for estimating a population mean, or the difference between two populations means, etc.

Back 64

t distribution

Front 65

t*:

Back 65

The multiplier of standard error in computing margin of error for estimating a mean (or the difference between two means).. The value for t* is found on the t table in the intersection of the appropriate df row and level of confidence column

Front 66

Procedure used to assess the evidence against a claim (hypothesis) about the value of a parameter.

Back 66

Test of significance

Front 67

A number that summarizes the data for a test of significance; usually used to obtain P-value

Back 67

Test statistic

Front 68

: A statistical procedure used to compare the means from two populations either with a test of their equality or by estimating the difference between two population means.

Back 68

Two-sample t procedure:

Front 69

A test where the alternative hypothesis contains “does not equal”.

Back 69

Two sided test

Front 70

The error made when a true null hypothesis is rejected. (i.e. you reject H0 when H0 is true.)

Back 70

Type I error:

Front 71

The error made when a false null hypothesis is not rejected. (i.e. you fail to reject H0 when H0 is false.)

Back 71

Type II error

Front 72

A condition where the mean of all possible statistic values equals the parameter that the statistic estimates.

Back 72

Unbiased

Front 73

A test with “>” in the alternative hypothesis.

Back 73

Upper-tailed test (also called a right-tailed test)

Front 74

: The square of standard deviation. Sample variance is s2 and population variance is σ2.

Back 74

Variance