Stat Ch.5-9

Random sample

A sample produced by the random sampling technique.

Hypothesis test

A statistical method that uses sample data to evaluate a hypothesis about a population.

Standardized scores

Also known as z-scores and t-scores, these convert measures made on different scales to a standard score, enabling comparisons and combinations.

Percentile rank

Defined as the percentage of the individuals in the distribution who have scores that are less than or equal to the specific score.

A z-score beyond +/- 3.00 indicates that the score is extreme and is noticeably different from the other scores in the distribution. True/False?

False. +/- 2.00 indicates the score is extreme.

Central limit theorem

For any population with mean and standard deviation, the distribution of sample means for sample size n will have a mean of mu and a standard deviation of sigma/square root of n and will approach a normal distribution as n approaches infinity.

Probability

For any specific outcome, this is defined as a fraction or a proportion of all the possible outcomes.

Critical region

Is composed of the extreme sample values that are very unlikely (as defined by the alpha level) to be obtained if the null hypothesis is true.

What does the alt hypothesis predict?

It predicts that the independent variable (treatment) does have an effect on the dependent variable.

What does the null hypothesis predict?

It predicts that the independent variable (treatment) has no effect on the dependent variable (scores) for the population.

What does the standard error of M do?

It provides a measure of how much distance is expected on average between a sample mean (M) and the population mean (mu).

What does the estimated standard error provide?

It provides an estimate of the standard distance between a sample mean and the population mean.

Cohen's D

Measures the effect size and standardizes it.

Alternative hypothesis (H1)

States that there is a change, a difference, or a relationship for the general population.

Null hypothesis (H0)

States that there is no change, no difference, or no relationship.

Distribution of sample means

The collection of sample means for all of the possible random samples of a particular size (n) that can be obtained from a population.

Law of large numbers

The larger the sample size (n), the more probable it is that the sample mean is close to the population mean.

Sampling error

The natural discrepancy, or amount of error, between a sample statistic and its corresponding population parameter.

Deviation score

The numerator for the z-score formula (X-mu).

What does beta symbolize?

The probability of a Type 2 error

Alpha level/level of significance

The probability value that is used to define the concept of "very unlikely" in a hypothesis test.

Standard error of M

The standard deviation of the distribution of sample means = sigma w/M.

Raw score

These are original, unchanged scores that are the direct result of measurement.

Why are standardized distributions used?

They are used to make dissimilar distributions comparable.

Standardized distribution

This is composed of scores that have been transformed to create predetermined values for mu and lower case sigma.

Sampling distribution

This is when a distribution of statistics is obtained by selecting all of the possible samples of a specific size from a population.

Percentile

This is when a score is referred to by its percentile rank.

Expected value of M

This is when the mean of the distribution of sample means is equal to the mean of the population of scores, mu.

Statistically significant

This is when the result is very unlikely to occur when the null hypothesis is true.

One-tailed test

This is when the statistical hypotheses specify either an increase or a decrease in the population mean. That is, they make a statement about the direction of the effect.

Effect size

This measure is intended to provide a measurement of the absolute magnitude of a treatment effect, independent of the size of the sample(s) being used.

Type 2 error

This occurs when a researcher fails to reject a null hypothesis when you should, in fact, reject it.

Type 1 error

This occurs when a researcher rejects a null hypothesis that is actually true.

Random sampling

This requires that each individual has an equal chance of being selected and that the probability of being selected stays constant from one selection to the next if more than one individual is selected.

Simple random sample

This requires that each individual in the population has an equal chance of being selected.

z-score

This specifies the precise location of each X value within a distribution.

Test statistic

This term indicates that the sample data are converted into a single, specific statistic that is used to test the hypotheses.

Sampling with Replacement

To keep the probabilities from changing from one selection to the next, it's necessary to return each individual to the population before you make the next selection.

A z-score near 0 indicates that the score is close to the population mean and, therefore, is representative. True/False?

True

The z-score distribution will have the same shape as the distribution of raw scores, and it always will have a mean of 0 and a standard deviation of 1. True/False?

True

Independent random sample

When the second requirement is added that: if more than one individual is being selected, the probabilities must stay constant from one selection to the next.

Do z-scores provide an objective method for determining how well a specific score represents its population?

Yes

Unit normal table

complete listing of z-scores and proportions

Degrees of freedom

describes the number of scores in a sample that are independent and free to vary.

Remember the t-statistic uses ______

estimated standard error in the denominator

confidence interval

is an interval, or range of values, centered around a sample statistic.

t-distribution

is the complete set of t values computed for every possible random sample for a specific sample size (n) or a specific degrees of freedom (df).

Estimated standard error

is used as an estimate of the real standard error, when the value of sigma is unknown.

t statistic

is used to test hypotheses about an unknown population mean when the value of sigma is unknown.

What does the t-distribution do?

it approximates the shape of the normal distribution, especially for large samples or samples from a normal population.

Directional test hypothesis test is also known as a?

one-tailed test

The ____ of a statistical test is the probability that the test will correctly reject a false null hypothesis. That is, ____ is the probability that the test will identify a treatment effect if one really exists.

power; power

If sample data fall in the critical region, the null hypothesis is:

rejected

What are the parameters of the distribution of sample means?

shape, central tendency, and variability

What happens to the sample variance when the df increases?

the better the sample variance represents the population variance

What happens to the t-statistic when the df increases?

the better the t-statistic approximates the z-score

estimated d

the calculated value of cohen's d.

The distribution of sample means is normal if:

the population from which the samples are selected is normal or the size of samples is thirty +

percentage of variance accounted for by the treatment (r squared)

when you remove the treatment effect that reduces the variability

The sign of the z-score indicates ____

whether the location is above the mean (positive) or below the mean (negative).