Stats test 2! CHAPTER 6,7,8.

larger standard deviation..

the larger the standard error

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.

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.

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 hypothesis by determine the likelihood that a sample statistic would be selected if the hypothesis regarding the population parameter were true

sampling without 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

sampling

is to behavioral

theoretical

is to statistics

experimental sampling

most used in behavioral research the order of selecting individuals does not matter, and each individual selected is not replaced before selected again

sample variance

on average the ___________ is equal to the population variance when we divided SS by df. this makes the ______ an unbiased estimator of the population variance.

sampling with replacement

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.

nondirectional tests

are used to test hypothesis when we are interested in any alternative in the null hypothesis. most common test in behavioral science. -more conservative -eliminates possibility of type 3 error

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 with 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 it is false.

level of significance

is a criterion of judgement upon which a decision is made regarding the value stated in a null hypothesis. The criterion is based on the probability of statistic measured in a sample if the value stated in the null hypothesis were true.

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 a given size from the same population

z statistic

is a 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

sample design

is a plan for how individuals will be selected from a population of interest. addresses two questions 1. does the order of selecting participants matter? 2. do we replace each selection before the next draw

null hypothesis

is a statement about a population parameter, such as the population mean that is assumed to be true. is a starting point. We will test whether the value stated in the _____ is likely to be true

hypothesis

is a statement or proposed explanation for an observation, a phenomenon or a scientific problem that can be tested using the research method. Is often a statement about the value of a parameter in a population

alternative hypothesis

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

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

sample mean

is an unbiased estimator of the value of the population mean

unbiased estimator

is any sample statistic obtained from a randomly selected sample that equals the value of its respective population parameter on average. the sample mean is an ________ because it equals the population mean on average.

effect

is the difference between a sample mean and the population mean stated in the null hypothesis. n hypothesis testing, an effect is not significance when we retain the null hypothesis; an effect is significance when we reject the null hypothesis.

sampling eror

is the extent to which sample means selected from the population differ from one another. This difference, which occurs by chance, is measured 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 a terror that we will allow and still decide to reject the null hypothesis. (usually is.05)

p value

is the probability of obtaining a sample outcome. given that the value stated in the null hypothesis is true. the ____ for obtaining a sample outcome is compared to to the level significance.

type 1 error

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

type 2 error/beta

is the probability of retaining a null hypothesis that is actually false. -is the probability of incorrectly retaining the null hypothesis.

rejection region

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

standard error of the mean

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

obtained value

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

law of large numbers

states that increasing the number of observations or samples in a study will decrease the standard error. hence, larger samples are associated with closer estimates of the population mean on average.

4 steps to hypothesis testing

step 1: state the hypothesis step 2: set the criteria for a decision step 3: compute the test statistic step 4: make a decision

theoretical sampling

the order of selecting individuals matters, and each individual selected is replaced before sampling again uses for statistical theory

three characteristics of the sample mean

1. the sample mean is an unbiased estimator. On average, the sample mean we obtain in a randomly selected sample will equal the value of the population mean 2. a distribution of sample means follows the central limit theorem. That is, regardless of the shape of the distribution in a population, the distribution of sample means selected from the population will approach the shape of a normal distribution, as the number of samples in the sampling distribution increases. 3. a distribution of sample means has minimum variance. the sampling distribution of sample means will vary minimally from the value of the population mean

standard error

_____ of the mean is the standard deviation of the sampling distribution of sample means

the variance

________ of skewed distribution can be any positive number.

directional/one tailed test

are hypothesis tests in which the alternative hypothesis is stated as greater than (>) or (<) less than. Hence, the researcher is interested in a specific alternative in the null hypothesis. -difficult to justify -greater power -do not double the probability number

statistical significance

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