Exam 4 - general flash cards

_____ Distributions: Frequency distributions based on real data

(observed data) from actual research.

Empirical

______ Distributions: Frequency distributions based on

mathematical formulas and logic rather than empirical observations.

Theoretical

What are empirical distributions based on?

observed data

What are theoretical distributions based on?

math formulas and logic

Theoretical Distributions are used in statistics to determine

____.

probabilities

When there is correspondence between an empirical

and theoretical distribution, you can use theoretical distribution to

make predictions about ?

future empirical events

Probability Value: ? to ?

0.00; 1.00

Probability value:

p = ?, no chance event will happen

p = ?, event is certain to happen

0.00; 1.00

____ Distribution: Occurs when frequency of each value on the

x-axis is the same (all scores have the same frequency).

Rectangular

The chance of choosing cards out of a deck is a ______ distribution

rectangular

_____ Distribution: Distribution of frequency of events that can only

have two possible outcomes.

Binomial

Flipping a coin, heads or tails is a _______ distribution

binomial

Characteristics of a normal distribution - (there’s 7)

1. No _____

2. _______ & bell-shaped

3. X-axis consists of standardized ______

4. Mean of distribution, μ = _

5. Standard deviation, σ = __

6. ____, _____, and _____ are the same score

7. Two inflection points, where direction changes are at ____ and ____ standard deviations

1. No y-axis

2. Symmetrical & bell-shaped

3. X-axis consists of standardized Z scores

4. Mean of distribution, μ = 0

5. Standard deviation, σ = 1.0

6. Mean, Median, Mode are the same score

7. Two inflection points, where direction changes are at -1.0 and 1.0 standard deviations

When empirical distributions are “changed” to normal distributions, they

have a mean of ____ and a standard deviation on _____

0; 1.0

_______ Statistics: Uses samples to estimate something about a

population parameter above what can possibly happen by chance

Inferential

The best sample…

● Leads to ?

● Is representative of ?.

● Is a _____ sample!

● Leads to correct decisions about the target population.

● Is representative of the target population.

● Is a RANDOM sample!

A random sample is one in which ALL members of the population

have an _________ of getting selected as members of the

sample.

____ CANNOT be random!

Humans

a ______ is seen as being the best method for generalizing to a population. It’s also Mathematical & objective

Random Numbers Table

A _____ sample is one obtained by method that systematically

under selects or over selects from certain groups in the population.

biased

characteristics of a sample ____ sample….

Population members do NOT have an equal chance of selection.

Increases chance that sample is unrepresentative!

biased

A research sample is obtained using a _____-experimental design, in

which _____ ________ to experimental groups is used.

quasi; random assignment

is sampling distributions -

● Standard Deviation = ______

● Mean = ______

Standard Error; Expected Value

important characteristics of a sampling distribution:

Important Characteristics

1. Every sample is drawn ______ from the ______.

2. _______ is the same for all samples.

3. The number of samples is _____.

4. The _____ is calculated for each sample.

5. The sample means are arranged into a ______ distribution

1. Every sample is drawn randomly from the population.

2. N (sample size) is the same for all samples.

3. The number of samples is large.

4. The mean is calculated for each sample.

5. The sample means are arranged into a frequency distribution

The central limit theorem (CLT) states that - For any population, the sampling distribution of the mean will approach a normal distribution as ?

sample size (N) gets larger.

in regard to the CLT - the sampling distribution of the mean will have:

○ Mean expected value equal to the __.

○ Standard error equal to ?

μ (population mean)

standard deviation divided by the square root of N.

The CLT works EVEN when original population is NOT ?

Normally distributed

What is the minimum sample size required for experiments?

N ≥ 30

for the CLT - If you take sufficiently large samples from a population, the samples’ ______ will be normally distributed, even if the population isn’t normally distributed.

means

= the number of values that are free to vary after you've used some information (or imposed a constraint).

Degrees of freedom (df)

_________ is a range of scores from low to high with the

mean of the sample in the middle of the interval.

Confidence Interval (CI)

Each CI has a?

Upper and lower limit

CI statistic can be used to determine if the calculated sample mean is

truly representative of the ?

true population mean (μ).

How can you be certain to which what degree of confidence do you believe you have captured within the interval?

Using CI

_____ Testing: Used by researchers to support beliefs about

comparisons (i.e. variables or groups).

Hypothesis

● ____________: Equality hypothesis; statement comparing two

statistics (usually two means).

● ________ Difference hypothesis; statement

comparing two statistics or groups, suggesting there is a difference.

Null Hypothesis (H₀)

Alternative Hypothesis (H₁)

Steps of Hypothesis Testing:

• Write the _________ (H₀).

• Write the _________ (H₁).

• Set _______ level (amount of error allowed) and determine degrees of

• freedom and critical test value.

• Pick and calculate the significance test that fits your design.

• Decision: _________

Write the null hypothesis (H0).

Write the alternative hypothesis (H1).

Set alpha level (amount of error allowed) and determine degrees of

freedom and critical test value.

Pick and calculate the significance test that fits your design.

Decision: Accept/Reject the null

_________ t-Test: Used when one needs to compare a sample mean to a

population mean.

one sample

_______ - Decision to reject null when in fact, null is true.

Type I Error

_______ Error - Decision to accept null when in fact, alternative is true.

Type II

A more stringent ______ level (α = 0.01 vs α = 0.05) decreases likelihood

of Type I Error but increases likelihood of Type II Error.

alpha

A more stringent alpha level (α = 0.01 vs α = 0.05) decreases likelihood

of Type Error but increases likelihood of Type __ Error.

I

II

The probability of making a Type I Error = ______ and probability of

making a Type II Error = ____

alpha (α); beta (β)

● α and β are ____ related

inversely

Alpha level is also known as the level of _____

significance

_____ level is the probability of rejecting the null hypothesis when the null hypothesis is true. Probability of making the “_____”

Alpha; wrong decision

α = _____ is the standard alpha level because it “provides a great deal

of protection from Type I Errors”

0.05

● A more stringent alpha level is α ≤ _____

0.05

p or P value (p < 0.05), is the probability of the data obtained (t-obtained),

if the null hypothesis is ___.

true

_____ level is used to refer to a pre-chosen probability and ____ is used

to indicate a probability that you calculate after a given study.

alpha; p-value

______: Researchers set alpha level and decide if they are

computing a one-tail or two-tail test before data are measured and

collected.

a priori

What are the three types of alternative hypothesis?

two tailed, one-tailed (left sided), and one tailed (right sided)

_______ is a calculation that allows us to answer the

question: “How much difference is there?” or “How meaningful is the

difference?”

Effect Size Index

Interpreting Effect Size:

● d < .20 = ____

● d = .20 - .49 = ____

● d = .50 - .79 = _____

● d = .80 + = _____

meaningless

small

medium

large

Paired Samples are dependent/correlated samples. We expect to find a

_____ relationship between the groups on the variable of interest

(dependent variable)

linear

three types of correlated studies:

Natural, matched, and repeated

_______ _____: Subjects are not assigned to groups; they exist in groups

naturally

Natural pairs

______ ______ : Researcher assigns subjects to groups based upon

some variable/characteristic to balance or control the effects of

extraneous variables.

matched pairs

_____ ______ : More than one measure (of DV) is taken on each

subject; often a pretest/post-test scenario

Repeated Measures

Independent Samples are __________. We do NOT assume groups

are correlated (linearly related).

between-subjects

The t-test is used to determine if the two

populations of interest have the same ____.

mean

● In _______, we computed confidence interval to determine

if we capture the true μ within the lower and upper limits.

● In ________, we determine whether zero is

captured between LL and UL.

one-sample design; two-sample confidence interval

If zero is captured between LL and UL, there____ significant

difference between the two means

is NO

If zero is NOT captured between LL and UL, there ______a significant

difference between the two means.

IS

_________: The ability to reject null when it’s truly false. Numerical

expression

Statistical Power

Power = ?

1 - β

_______ is the probability of making a type 2 error, so 1-B = ?

B (beta)

The probability of not making a type 2 error

Power is the the probability of NOT making a Type II Error. So, the

more power you have, the more likely you are to ______

when it is really false.

Reject H₀

Factors that Affect Statistical Power:

Effect size, standard error of the difference, sample size, and alpha level

The ______ the effect size, more likely to reject H_o.

larger

Significance test denominator; The ______ the error, more likely to reject Ho

smaller

The ____ the sample size, more likely to find a difference if true difference exists.

larger

The ______ alpha is, more likely to reject Ho.

alpha

The ____ sets the range, your must be in that range of you will need to reject the hypothesis and accept the ____ hypothesis

T_c; T₀

null; alternative

if you retain, the P __ .05

> (greater than)