PT 451 Statistical Inference

population

entire group of people that you're studying

sample

actual group of people that you're studying

normal curve

The frequency distribution of a continuous trait in population is assumed to approximate a _______________ ___________ (bell curve)

frequency distribution

plot of the count for different values of a trait

68.3%

μ ± 1σ contains what percentage of all values in a normal distribution?

99.7%

μ ± 3σ contains what percentage of all values in a normal distribution?

95.5

μ ± 2σ contains what percentage of all values in a normal distribution?

± 1.96 σ

95% of all values in a normal curve will fall within what value?

t-distribution

The frequency distribution of a continuous trait in a sample is assumed to approximate what curve?

t-distribution is flatter

difference between t-distribution and a normal distribution

False (Each sample size has its own t-distribution)

True or false? T-distribution remains the same among different sample sizes as long as the variable being measured stays the same

wider, flatter

Describe t-distributions for smaller samples

smaller

When sample size decreases, each standard deviation from the mean includes a smaller or larger proportion of the values in the the t-distribution

decreases

The number of standard deviations decreases or increases as sample size increases within a specific percentage of all the values in a distribution

number of values free to vary

degrees of freedom

sampling error

mismatch of mean and standard deviation between sample and population

False (always occurs)

sampling error only occurs when you collect an inaccurate sample. True or False?

standard error of the mean

error associated with our sample mean

decreases

what happens to the SEM when sample size decreases regardless of whether s stays the same?

confidence intervals

How do we account for sampling error

95%

most common CI

population

Range of values we are 95% confident contains the estimated sample or population parameter?

False

True or false? The 95% CI is the range of values that contains 95% of all the values

False (we can not "prove" anything. only "disprove").

To prove something, we test where two groups are the same. True or False?

null hypothesis

what do we formulate to test whether two groups are the same?

alternative hypothesis

What do we accept if we disprove the null hypothesis?

No (we only "fail to reject")

Should we ever technically "accept" a hypothesis?

dichotomous

What kind of outcome is produced from inferential statistic

null hypothesis

Inferential statistics estimate the probability that the _________________________ is correct

p-value

the probability of observing
some effect under H₀ (i.e., purely by chance)

mean difference, standard deviation, sample size

what three things is the p-value based on?

high

When effects are small, variable, and derived from a small sample size, the p-value is high or low?

directional hypothesis

a hypothesis that makes a specific prediction about the direction of the relationship between two variables

nondirectional hypothesis

research hypothesis that does not predict a particular direction of difference between the population like the sample studied and the population in general

one-tailed

What kind of statistical tests do we use with directional hypotheses?

one-tailed

Do one-tailed or two-tailed have lower critical values?

Type I errors

Error occurring when we reject the null hypothesis, but it is actually true (false positives)

Type II errors

Error occuring when we accept the null hypothesis, but it is false

Type 1

Which error is more serious? Type 1 or Type 2?

significance level

The rate of Type I errors is set by what parameter of inferential statistics.

significance level α

The p-value that we are willing to accept in order to reject H₀

0.05

What is the most common value for α?

critical value

represents how many standard errors that two scores must be from one
another to be considered differen

larger

When we calculate a t-statistic, if it is
_____________ than this critical value, then we reject H₀

power

The rate of Type II errors is set by what parameter of inferential statistics.

β

The probability of making a Type II error is defined as ____

0.2

most common value for β

1-β (0.80)

Power formula

α, variance, sample size, and effect size

Power is a function of what 4 things?

power analysis

a statistical method to determine the acceptable sample size that will best detect the true effect of the independent variable

priori power analyses

a statistical method that helps researchers determine the minimum sample size needed for a study to detect an effect with a certain level of confidence. It's performed before data collection begins as part of the research planning process

post hoc power analysis

power analysis conducted after a study

minimal detectable effect

represents the smallest effect that a statistical test can detect.

central limit theorem

Tells us that as we sample a population, the frequency distribution for sample means will approximate a normal distribution, even for skewed
population distributions.

True (central limit theorem)

It is possible to apply inferential statistics based on normal curves to skewed variables. True or False?

True

Larger samples are likely to give more consistent sample means that are closer to the true population mean. True or False?

parametric statistics

Statistics that assume we can estimate population parameters from our sample

1. data derived from known sampling distribution
2. data points are independent observations
3. close variances
4. Interval and ratio data

4 assumptions of parametric statistics

nonparametric statistics

do not try to estimate population parameter; don't assume that the
population follows a known sampling distribution.

distribution-free statistics

another name for nonparametric statistics

too small sample size, nominal or ordinal data,

When should you use nonparametric statistics?

z-test, one-sample t-test

statistical test used to compare a sample to the population

population mean, population standard deviation

What does a z-test use in its calculation?

hypothetical mean, sample standard deviation

What does a one-sample t-test use in its calculation?

standard errors the sample mean differs from the population mean

The z or t statistic represents what?

1.65

test statistics exceeding what value in one-tailed experiments are considered extreme enough to reject the H₀

1.96

test statistics exceeding what value in two-tailed experiments are considered extreme enough to reject the H₀