Psych Stats Unit 2

Alternative Hypothesis

(H1) States that there is a change, a difference, or a relationship for the general population. In the context of an experiment, H1 predicts that the independent variable does have an effect on the dependent variable

Null Hypothesis

(Ho) States that in the general population there is no change, no difference, or no relationship. In the context of an experiment, Ho predicts that the independent variable (treatment) has no effect on the dependent variable (scores) for the population

Estimated Standard Error

(S_M) Used as an estimate of the real standard error σM when the value of σ is unknown. Provides an estimate of the standard distance between a sample mean and the population mean

Sampling Distribution

A distribution of statistics obtained by selecting all of the possible samples of a specific size from a population

Probability

A fraction or a proportion of all the possible outcomes

Level of Significance/ Alpha Level

A probability value that is used to define the concept of "very unlikely" in a hypothesis test and shows the probability of a Type I Error

Significant

A result is said to be this if it is very unlikely to occur when the null hypothesis is true

Hypothesis Test

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

Confidence Interval

An interval centered around a sample statistic that describes the amount of uncertainty associated with a sample estimate of a population parameter.

Standardized Distribution

Composed of scores that have been transformed to create predetermined values for μ and σ. Used to make dissimilar distributions comparable

Critical Region

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

Degrees of Freedom

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

Beta

Greek letter, used as the symbol to represent the probability of a Type II error

Test Statistic

Indicates that the sample data are converted into a single, specific statistic that is used to test the hypothesis

Effect Size

Intended to provide a measurement of the absolute magnitude of a treatment effect, independent of the size of the samples being used

Unit Normal Table

Lists proportions of the normal distribution for a full range of possible z-score values

Type II Error

Occurs when a researcher fails to reject a null hypothesis that is really false.

Type I Error

Occurs when a researcher rejects a null hypothesis that is actually true.

Cohen's d

One of the simplest and most direct methods for measuring effect size. Measures the distance between two means

Raw Score

Original, unchanged scores that are a direct result of measurement

Percentile Rank

Percentage of the individuals in the distribution who have scores that are less than or equal to the specific score

Simple Random Sample

Requires that each individual in the population has an equal chance of being selected

Random/Independent Sample

Sample obtained when: It is required 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

Z-Score/ Standardized Score

Specifies location of each X value within a distribution.

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

t Distribution

The complete set of t values computed for every possible random sample for a specific sample size or a specific degrees of freedom. Approximates the shape of a normal distribution

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

Expected Value of M

The mean of the distribution of sample means is equal to the mean of the population μ

Sampling Error

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

Power

The probability that the statistical test will correctly reject a false null hypothesis.

Standard Error of M

The standard deviation for the distribution of sample means. Provides a measure of how much distance is expected on average between a sample mean M and the population mean μ

Directional Test/ One-Tailed test

The statistical hypotheses (H0 and H1) specify either an increase or decrease in the population mean.

Sampling with Replacement

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

Z-Score Transformation

Transforming every X value in a distribution into a corresponding z-score

t Statistic

Used to test hypotheses about an unknown population mean, μ , when the value of σ is unknown.

Estimated d

Used when the population values aren't known and you substitute the corresponding sample values in their place

Deviation Score

measures the distance in points between X and μ and indicates whether X is located above or below the mean

(r^2)

percentage of variance accounted for by the treatment

Central Limit Theorem

the sampling distribution of the mean of any independent, random variable will be normal or nearly normal, if the sample size is large enough

Percentile

when a score is referred to by its percentile rank the score is called a __________