Stats

What is a hypothesis test and what is the goal?

Hypothesis testing is a statistical method that uses sample data to evaluate a hypothesis about a population The goal is to rule out chance (sampling error) as a plausible explanation for results

How can the Z-Score for a sample mean be used to obtain probabilities?

Find out of our sample mean is similar to the greater population

What steps must be taken to find the proportion of scores the fall between to Z-Scores?

Find the difference between the two separate scores and the mean located in column D and then add those two together

What symbol(s) are used to represent standard error?

For example, μ refers to a population mean; and x, to a sample mean. σ refers to the standard deviation of a population; and s, to the standard deviation of a sample

What is the role of probability in inferential statistics?

Helps you find out likelihood of drawing specific samples.

4th element of hypothesis testing

test statistic

In a hypothesis testing situation, what is the probability of making a type 1 error?

the alpha level

Sampling error

the amount of error between a sample statistic and its corresponding population parameter

distribution of sample means

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

sampling error

the difference between the results of random samples taken at the same time

what should the percentile rank equal to?

should = scores equal to or below

What value must the proportion of scores above and below a particular Z-Score add up to?

1

How does probability relate to proportion?

Probability is defined as a fraction or a proportion

What does the sign of a Z-Score tell us?

(+/-) tells us the direction of the score below or above the mean

what are some concerns about the null hypothesis?

1. Absolute all-or-none decision 2. Null hypothesis is artificial- states that there is no treatment effect 3. Significant vs. Substantial

3 Concerns of Hypothesis testing

1. Absolute, all-or-none decision 2. Null hypothesis is artificial 3. Significant vs. Substantial

5 Elements of hypothesis testing

1. Hypothesized population parameter 2. Sample statistic 3. Estimate of Error 4. Test statistic 5. Alpha level

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

1. The difference between sample and population can be explained by sampling error 2. the difference is too large to be due to sampling error

What are 3 sources of variance introduced in lecture?

1. treatment effect 2. individual difference (sampling error) 3. experimental error

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

1.Mean, median, mode= the same 2.mean is equal to population mean of raw scores 3.mean of sampling distribution= expected value of the "mean"

What is the unit normal table?

A list of several different proportions corresponding to different Z-Scores

Probability

A number that describes how likely it is that an event will occur

what is the difference between standard deviation and standard error?

A standard deviation is a measure of variability for a distribution of scores in a single sample or in a population of scores. A standard error is the standard deviation in a distribution of means of all possible samples of a given size from a particular population of individual scores.

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

Body, because those will be all the scores that scored worse than the positive score

1st concern of hypothesis testing

Absolute, all-or-none decision

How are alpha and critical value different?

Alpha is probability that is used to determine concepts of very unlikely critical value is composed of extreme sample values that are very unlikely to be obtained

When is sampling error a problem?

Always -when ever you are using samples

What is the relationship between sample size and standard error?

As sample size increase, the standard error decreases *Larger samples= more accurate

How are alpha and critical value the same?

Both contain unlikely scores or score and alpha is the probability of the critical value

Step 3 of Hypothesis Testing

Collect and analyze data

Step 5 of Hypothesis Testing

Describe what happened

What do Z-Scores tell us about an individual score?

Exactly where the score is located relative to all other scores

When is it appropriate to use a directional hypothesis test?

If a researched predicts a specific direction for the treatment effect

the distribution of a sample means must satisfy at least one of two specific criteria for the unit normal table to be used appropriately?

If the population for where the means come for are normal and if the sample size is > 30

In what hypothesis testing situations would it be appropriate to preform a Z-Score test?

If you know the population mean and the population standard deviation

Effect size

Increased to provide a measurement of the absolute magnitude of a testament effect independent of the size of the samples being used

Define probability

Likelihood

step 4 of hypothesis testing

Make a decision

How do you randomly choose a score from a numeral distraction, what score are you most likely to select?

Mean

Cohens D

Measures the size of the mean difference in terms of the standard deviation

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

Normal if n> 30 -always normal even if raw scores are not

2nd concern of hypothesis testing

Null hypothesis is artificial

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

Population means are not equal

Normal Distribution

Precisely defined and always the same shape

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

RAW | Z-SCORES Shape: normal/normal Central tendency: varies/always 0 Variability: varies/ Z= 1 = 1 SD

Type 1 error

Researcher concluded that a treatment does have an effect when it has no actual effect

Step 2 of Hypothesis Testing

Set criteria

3rd concern of hypothesis testing

Significant vs. Substantial

What are some synonyms for the Z-Score for sample means?

Single- sample Z-Test or Z-test

How is the critical region defined?

Siple outcomes that are very unlikely to occur if the treatment has no effect (null hypothesis is true)

Step 1 of Hypothesis Testing

State hypothesis

What is the Law of Large Numbers?

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

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

Tail, Because the tail will hold all of the scores that are at or worse than the given score

When evaluating differenced between or among means, what does the null hypothesis always sate?

That there is no difference

Standard error

The average distance between sample means and population means

Standard deviation

The average distance between the score and the mean

What is the distribution of sampling means?

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

What does the Z-Score for a sample mean tell us?

The exact location of any specific score and exactly where that score is located

alternative hypothesis

The hypothesis that states there is a difference between two or more sets of data.

Define the expected value of M

The mean of the population distribution of sample means is equal to the mean of the population of scores and is called the expected value of M

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

The population mean

Power

The probability of correctly rejecting a false null hypothesis

What are sources for variance?

Things that make the mean different

How do you find the z score of a sample mean?

To find the Z score of a sample, you'll need to find the mean, variance and standard deviation of the sample. To calculate the z-score, you will find the difference between a value in the sample and the mean, and divide it by the standard deviation.

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

To reject or fail to reject the null hypothesis

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

We expect the sample means to be close to the population mean

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

We reject or fail to reject the null greater of less than critical value

What does the absolute value of the Z-Score tell us?

Where the score is exactly located

type 11 error

a "miss" in the statistical inference process, in which researchers conclude that there is no effect in a population when there really is one

effect size

a measure of the strength of the relationship between two variables or the extent of an experimental effect

two-tailed test

a method in which the critical area of a distribution is two-sided -tests whether a sample is greater than or less than a certain range of values

one-tailed test

a one-tailed test tells you the effect of a change in one direction and not the other -only interested in one direction

null hypothesis

a statement or idea that can be falsified, or proved wrong

statistical significance

a statistical statement of how likely it is that an obtained result occurred by chance

5th element of hypothesis testing

alpha level p < .05 p < .01 p < .001

hypothesis test

an assumption that we make about the population parameter

critical values/critical region

cut-off values that define regions where the test statistic is unlikely to lie -for example, a region where the critical value is exceeded with probability/alpha if the null hypothesis is true.

What equation is used to compute the standard error of M?

estimate

3rd element of hypothesis testing

estimate of error -variability -sample size

Example of inferential statistics

ex. people with higher scores on a test of mental ability perform their jobs better than those with lower scores, or that team members in small teams are happier with their work than team members in a large teams • testing an hypothesis or theory

1st element of hypothesis testing

hypothesized population parameter

Statistically significant

means that the null hypothesis has been rejected, which means that the result is very unlikely to have occurred nearly by chance

z-scores

measure the distance of a score from the mean in units of standard deviation

What symbol is used to represent the null hypothesis?

often denoted H0, pronounced as "H-nought", "H-null", or "H-zero" (or, even, by some, "H-oh"), with the subscript being the digit 0.

What are 2 thing that a researcher can do to increase power?

pick a smaller alpha level Change something to decrease type 1 error

what does alpha define in terms of?

probability

when the z-score is positive, what does the percentile rank equal?

proportion in body

when the z-score is negative, what does the percentile rank equal?

proportion in tail

alpha

refers to significance level , the probability of making a Type I error

Type 1 error

rejecting a true null hypothesis

2nd element of hypothesis testing

sample statistic

Power (stats)

the probability that the test rejects the null hypothesis when a specific alternative hypothesis is true. -The statistical power ranges from 0 to 1, and as statistical power increases, the probability of making a type II error decreases

standard error

the standard deviation of a sampling distribution

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

turn the score into a Z-Score then look at the tail or body of because the percentile rank for a score in a normal distribution is the proportion to the left of the score

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

we can compute the raw score value by the formula, x= µ + Zσ, where µ equals the mean, Z equals the z score, and σ equals the standard deviation.

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 deviations from the mean

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 T = (X - μ) / [ σ/√(n) ]. This makes the equation identical to the one for the z-score; the only difference is you're looking up the result in the T table, not the Z-table. For sample sizes over 30, you'll get the same result.

what does critical value define in terms of?

z-scores