Psych Stats 241 Exam 2 (ch 5,6,7,8)

What is the normal distribution?

Precisely defined and always the same shape, the mean is exactly in the middle, the mean, median, and mode are all the same value

If you randomly choose a score from a normal distribution, what score are you most likely to select?

The Mean

If you randomly choose a score from a data set, how far away from the mean is that score likely to be?

Within one standard deviation of the mean

What do z-scores tell us about an individual score?

The distance and direction from the mean where the score is located relative to all other scores

What equation is used to compute a z-score? How does this equation differ for population data compared to sample data?

z = x - μ / σ (population)

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z= X-M/s (sample)

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Both do the same thing, different symbols are used

What does the sign of the z-score tell us?

if the value is above or below the mean

What does the absolute value of the z-score tell us?

the number of standard deviations between the score and the mean

What equation is used to transform a z-score back to a raw (x) score?

x \= μ +z σ

How do raw (normal) distributions compare to z-score distributions in terms of shape, central tendency, and variability?

Raw: normal shape, central tendency varies, variability varies

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Z-score: normal shape, central tendency is always 0, variability- z=1=1SD

Define probability

Method for measuring and quantifying the likelihood of obtaining a specific sample from a specific population Probability \= Likelihood

How does probability relate to proportion?

Probability is equivalent to proportion

What is the role of probability in inferential statistics?

Probability forms a direct link between samples and populations

What is the unit normal table?

Table that lists proprtions of the normal distribution for a full range of possible z-score values

What value must the proportion of scores above and below a particular z-score sum up to?

Must sum up to one

How do we use the unit normal table to find the percentile rank for a particular score

Finding the score that is in the body

What steps must be taken to find the proportion of scores that fall between 2 z-scores?

Find the amount that falls below both scores and subtract them

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EX: 2 scores of -1 & -1.5

Z= -1 below= -.1587

Z= -1.50 below= .0668

.1587-.0668=.0919

If a z-score is positive, does the percentile rank for that score correspond to the proportion of scores found in the body or tail of a distribution? why?

body

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percentile rank for a specific x value is the percentage of individuals with scores at or below that number

If a z-score is negative, does the percentile rank for that score correspond to the proportion of scores found in the body or tail of a distribution? why?

tail

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percentile rank for a specific x value is the percentage of individuals with scores at or below that number

Define sampling error

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

When is sampling error a problem?

any time inferential statistics is used

What is the distribution of sampling 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

What 3 basic characteristics of the distribution of sampling means does the central limit theorem address?

shape, central tendency, and variability

What do we know about the shape of the distribution of sampling means?

it is normal is n is greater than 30

What do we know about the measures of central tendency for the distribution of sampling means?

the sample means should pile up around μ

What measure do we use to describe the variability for a distribution of sampling means?

standard error

Define the expected value of M

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

Define the standard error of M

The standard deviation of the distribution of sample mean, provides a measure of how much distance is expected on average between a sample mean and the populaiton mean

How does standard error differ from standard deviation?

SE- measures level of error distribution with sample and population mean

SD- measures dispersion around mean score and population

What is the relationship between sample size and standard error?

SE provides a way to measure the average (or standard) distance betweens sample mean and population mean

What is the law of large numbers?

States that the larger sample size the more probable it is that the sample mean is close to the population mean

What is the general form/ratio that inferential test statistics take? What does the numerator measure? What does the denominator measure?

test statistic: obtained difference (difference between means)/ difference expected by chance (measure of standard error)

What are some synonyms for the z score for sample means?

single sample z test, z test

What does the z score for a sample mean tell us?

if the sample means is in the critical region

How can the z score for a sample mean be used to obtain probabilities?

by using the unit normal table

The distribution of sample means must satisfy at least one for two specific criteria for the unit normal table to be used appropriately. What are these two criteria?

Sample is greater than 30 or a normal population

What is a hypothesis test? What is the goal of hypothesis testing?

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

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goal is to determine if the treatment has any effect on the individuals in the population

If we observe a treatment difference in a research study, what are two possible explanations for this difference?

the treatment has no effect

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has sample type one error

When evaluationg differences between or among means, what does the null hypothesis always state?

in the general population there is no change, no difference, no relationship

When evaluating differences between or among means, what does the alternative hypothesis always state?

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

When is it appropriate to us a directional hypothesis test?

if the research predicts cetain direction for the treatment effect

What are sources of variance?

anything that can lead to a difference in the means

What 3 are sources of variance introduced in lecture?

expeimental error, individual difference error, treatment effect

How are alpha and critical value the same? How do they differ?

alpha level: probability value used to define concept of very unlikely in a hypothesis test

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critical region: composed of extreme sample values that are very unlikely (as defined by alpha level) to be obtained if the null hypothesis is true, boundaries of the critical region are determined by the alpha level

How is the critical region defined?

composed of extreme sample values that are very unlikely (as defined by alpha level) to be obtained if the null hypothesis is true, boundaries of the critical region are determined by the alpha level

What are the two possible choices that can be made when making a decision about the outcome of a hypothesis test?

the treatment has an effect

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the treatment does not have an effect

Define statistically significant

if it is very likely to occur when null hypothesis is true the results are significant enough to reject the null hypothesis, 2 SD

How do we determine whether we have obtained a statistically significant difference?

if the z score is larger than the Zcv

IN what hypothesis testing situations would it be appropriate to perform a z test?

if there is information about population mean and SD

Define Type I error

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

Define type II error

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

What are some concerns about null hypothesis testing?

absolute all or none decision

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Null hypothesis is artificial

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significant vs. substantial

Define effect size

provide a measurement of the absolute magnitude of a treatment effect

What does Cohen's d measure?

the effect size

How is Cohen's d computed for z-tests?

d\= mean difference/standard deviation

How is Cohen's d evaluated?

small effect- mean difference less than 0.2 SD

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medium effect- mean difference around 0.5 SD

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large effect- mean difference greater than 0.8 SD

Define power

the probability of correctly rejecting a false null hypothesis

What are two things a researcher can do to increase power?

one tailed tests, and increase the alpha level