Behavioral Stats Exam 2

The null hypothesis

stated as the null is a statement about a population parameter such s the population mean that is assumed to be true The Null hypothesis is a starting point. We will test whether the value stated in the null hypothesis is likely to be true

Two outcomes A and B are independent

when the probability of one outcome does not affect the probability of the second outcome

Conditional Outcomes

when the probability of one outcome is dependent on the occurrence of the other outcome. An outcome is dependent when the probability of it occurrence is changed by the occurrence of the other outcome

Two outcomes A and B are complementary

when the sum of their probabilities is equal to 1.00. When two outcomes are complementary they are exhaustive of all possible outcomes so the two outcomes constitute 100% of the sample space

Mutally exclusive

when the two outcomes cannot occur together. the probability of tow mutually exclusive outcomes occurring together is 0

Unbiased estimator

any sample statistic, such as the sample variance when we divide SS by n-1, obtained from a randomly selected sample that equals the value of its respective population parameter, such as a population variance, on average

Nondirectional tests

are hypothesis tests in which the alternative hypothesis is stated as not equal to a value stated in the null hypothesis. Hence, the researcher is interested in any alternative to the null hypothesis

Cohen's effect size conventions

are standard rules for identifying small, medium, and large effects based on typical findings in behavioral research.

Real Limits

are the upper and lower values within which the probability of obtaining a binomial outcomes contained. The real limits for a binomial outcome, x, are x plus or minus 0.5

A bivariate random variable

is a random variable with only two possible outcome

Sample design

is a specific plan or protocol for how individuals will be selected or sampled from a population of interest

A Hypothesis

is a statement or proposed explanation for an observation, a phenomenon, or a scientific problem that inane be tased using the research method

Effect size

is a statistical measure of the size of an effect in a population which allows researchers to describe how far scores shifted in the population or the percent of variance that can be explained by a given variable

One-sample z test

is a statistical procedure test to test hypotheses concerning the mean in a single population with a known variance

Normal Distribution

is a theoretical distribution in which scores are symmetrically distributed above or below the mean, the median, and the mode at the center of distribution

The unit normal table

is a type of probability distribution table displaying a list of z scores and the corresponding probabilities associated with each z score listed

A random variable

is a variable obtained or measured in a random experiment unlike other mathematical variables a random variable is not the actual outcome of a random experiment but rather describes the possible as yet undetermined outcomes in a random experiment

z statistic

is an inferential statistic used to determine the number of standard deviations in a standard normal distribution that a sample mean deviates from the population mean stated in the null hypothesis

fixed event

is any event in which the outcome observed is always the same

Random event

is any event in which the outcomes observed can vary

For a single sample an effect

is the difference between a sample mean and the population mean stated in the null hypothesis. In hypothesis testing an effective is not significant when we train the null hypothesis an effect is significant when we reject to null hypothesis

A binomial distribution

is the distribution of probabilities for each outcome a variable with only two possible outcomes

a probability distribution

is the distribution of probabilities for each outcome of a random variable the sum of probabilities in a probability distribution is equal to 1.00

Sampling error

is the extent to which sample means selected from the sample population differ from one another. This difference, which occurs by chance is measure by the standard error of the mean

Alpha level

is the level of significance or criterion for a hypothesis test. It is the largest probability of committing a type I error that we will allow and still decide to reject the null hypothesis

Mathematical expectation

is the mean of a given random variable. The expected outcome of a random variable is the sum of the products fo each random outcome multiplied by the probability of its occurrence

P value

is the probability of a obtaining a sample outcome given that the value stated in the null hypothesis is true. The p value for obtaining a sample outcome is compared to the level of significance or criterion for making a decision

Type I error

is the probability of rejecting a null hypothesis that is actually true. Researchers directly control for the probability of committing this type of error

Type II error

is the probability of retaining a null hypothesis that is actually false

Probability

(symbolized as P) is the frequency of times an outcome occurs divided by the total number of possible outcomes

Directional Tests

Hypothesis tests where the alternative hypothesis is stated as "greater than" (>) or "less than" (<) a value stated in the null hypothesis. Hence, the researcher is interested in a specific alternative to the null hypothesis; also called one-tailed tests

Alternative hypothesis

Is a statement that directly contradicts a null hypothesis by statin that the actual value of population parameter is less than, greater than, or not equal to the value stated in the null hypothesis

Additive rule

P(A or B) = P(A) + P(B) - P(A and B) states that when two outcomes fo a given event are mutually exclusive the probability that any one of these outcomes occurs is equal to the sum of their individual probabilities

Sampling with replacement

is a method of sampling in which each participant or item selected is replaced before the next selection. This method of sampling is used in the development of statistical theory

A Type III error

a type of error possible with one-tailed tests in which a decision would have been to reject the null hypothesis, but the researcher decides to retain the null hypothesis because the rejection region was located in the wrong tail The "wrong tail" refers to the opposite tail from where a difference was overfed and would have otherwise been significant

Significance

describes a decision made concerning a value stated in the null hypothesis when the null hypothesis is rejected we reach significance. When the null hypothesis is retained we fail to reach significance

the standard normal distribution

is a normal distribution with a mean equal to 0 and a standard deviation equal to 1. The standard normal distribution is distributed in z score units along the x-axis

The central limit theorem

explains that regardless of the distribution of scores in a population, the sampling distribution of sample means selected at random from that population will approach the shape of a normal distribution, as the number of samples in the sampling distribution increases

Power

in hypothesis testing is the probability of rejecting a false null hypothesis. Specifically it is the probability that a randomly selected sample will show that the null hypothesis is false when the null hypothesis is indeed false

Level of Significance

is a criterion of judgment upon which a decision is made regarding the value stated in a null hypothesis. The criterion is based on the probability of obtaining a statistic measured in a sample if the value in the null hypothesis were true In behavioral science the criterion or level of significance is typically set at 5%. When the probability of obtaining a sample mean would be less than 5% if the null hypothesis were true then we reject the value stated in the null hypothesis

Critical value

is a cutoff value that defines the boundaries beyond which less than 5% of sample means can be obtained if the null hypothesis is true. Sample means obtained beyond a critical value will result in a decision to reject the null hypothesis

Sampling distribution

is a distribution of all sample means or sample variances that could be obtained in samples of given size from the same population

The Standard Z Transformation

is a formula used to convert any normal distribution with any mean and any variance to a standard normal distribution with a mean equal to 0 and a standard deviation equal to 1

Test statistic

is a mathematical formula that identifies how far or how many standard deviations a sample outcome is from the value stated in a null hypothesis. It allows researchers to determine the likelihood of obtaining sample outcomes if the null hypothesis were true. The value of the test statistic is used to make a decision regarding a null hypothesis

Bayes' Theorem

is a mathematical formula that relates to the conditional and marginal (unconditional) probabilities of two conditional outcomes that occur at random

Cohen's d

is a measure of effect size in terms of the number of standard deviations that mean scores shifted above or below the population mean stated by the null hypothesis. The larger the value of d the larger the effect in the population

The standard deviation of a probability distribution

is a measure of variability for the average distance that outcomes for a given random variable deviate from the expected value or mean of a probability distribution. It is calculated by taking the square root of the variance of probability distribution

The variance of probability distribution

is a measure of variability for the average squared distance that outcomes for given random variable deviate from the expected value or mean of a probability distribution

Hypothesis testing

is a method for testing a claim or hypothesis about a parameter in a population, using data measured in a sample. In this method we test a hypotheses by determine the likelihood that a sample statistic woods be selected if the hypothesis regarding the population parameter were true

Sampling with out replacement

is a method of sampling in which each participant or item selected is not replaced before the next selection. This method of sampling is the most common method used in behavioral research

Rejection Region

is the region beyond a critical value in a hypothesis test. When the value of a test statistic is in the rejection region, we decide to reject the null hypothesis; otherwise, we retain the null hypothesis

The Standard Error of the Mean

is the standard deviation of a sampling distribution of sample means. It is the standard error or distance that the sample mean values deviate from the value of the population mean

The sample space

is the total number of outcomes that can occur in a given random event

Obtained value

is the value of a test statistic. This value is compared to the crucial value(s) of a hypothesis test to make a decision. When the obtained value exceeds a critical value, we decide to reject the null hypothesis, otherwise we retain the null hypothesis

Z-score

is the value on the x-axis of a standard normal distribution. The numerical value of a score specifies the distance or the number or standard deviations that a value is above or below the mean

the multiplicative rule

states that when two outcomes for a given event are independent, the probability that both outcomes occur is equal to the product of their individual probabilities

Law of large numbers

stats that increasing the number of observations or samples in a stud will decrease the standard error. Hence larger samples are associated with closer estimates of the population mean on average