PSYC206 Test 2

Continuous Variable

A variable that can take any of an unlimited number of values in a given range, such as time, length, or weight.

Discrete Variable

A variable that can take only distinct or separated values, such as integers or counts of distinct items.

Standard Normal Distribution

A theoretical normal distribution with a mean ($\mu$) of $0$ and a standard deviation ($\sigma$) of $1$, usually displayed on a $z$ axis.

Population Parameters

Numerical values describing characteristics of a population, represented by Greek letters such as mean ($\mu$) and standard deviation ($\sigma$).

Sample Statistics

Numerical values calculated from a sample, represented by English letters such as sample mean ($M$) and sample standard deviation ($s$), used to estimate population parameters.

Random Sampling

A sampling method requiring that every member of the population has an equal probability of being selected and that all selections are made independently.

Sampling Distribution of the Sample Mean

The probability distribution formed by the means of many independent samples drawn from the same population.

Standard Error ($SE$)

The standard deviation of the sampling distribution of the sample mean, calculated using the formula $SE = \frac{\sigma}{\sqrt{N}}$.

Central Limit Theorem

A fundamental statistical theorem stating that the sum or mean of a number of independent variables has an approximately normal distribution, almost regardless of the original distribution shapes of those variables.

How many parameters are required to fully describe a standard distribution?

2, standard deviation and mean

To half SE, how much larger would N need to be?

4x

___________ is the standard deviation of the mean heap.

Standard Error

What does Confidence Interval ‘width’ depend on most out of these?

Standard Error

What is the best way to lower SE, create a narrower CI, and a narrow mean heap?

increase sample size

Central limit theorum is responsible for:

skewed or irregular population data producing standard distributed mean heaps

If N became 9 times larger, what would happen to SE?

It would become smaller by a factor of 3

Sample means tend to be normally distributed around the true population mean. The standard deviation of the distribution of sample means is:

SE

Which of the following is NOT an assumption to be able to use mean and SD:

Mean and Median cannot be the same value

Which of the following best describes a z-score

indicates how far a particular raw score is above or below the mean, in standard deviation units, when the population parameter is known

Which of the following can a z-score NOT do

Allow you to estimate a population mean from a sample mean

p=.05 is the scientific convention for

surprising or unlikely events

Sample statistics _______ population _________

estimate, parameters

Descriptions of a sample are called

statistics

Which of the following best describes sampling error

Statistics of random drawn samples will always deviate from the corresponding population parameters

Descriptions of a population are called

parameters

Sample statistics are:

Parameter estimates

Parameter estimates can be used:

to estimate the true population parameters

Random Sampling: selects a sample from a population such that each individual has a(n) ____ and _______ chance of being selected.

Equal, independant

Sampling Error reflects the fact that the statistics of _____ drawn samples will _____ the corresponding population parameters.

randomly, deviate from

I draw 8 samples from the same population that all have different SD’s and M, and don’t match the population they were drawn from. why?

Random sampling variablility

A population distribution is comprised of __________ and is defined by its ______ and _______.

Individual scores, mean, SD

A sample distribution is comprised of ________, it is defined by the ________ .

sample means, Standard error of the Mean

Why do sample distributions use standard error of the mean and not the SD like in population distributions?

because you are calculating the mean from groups of scores, not individual scores.

If a sample mean increases, the sample distribution will become ______

narrower

SEM is

the population standard deviation divided by the square root of the sample size

A population distribution consists of:

all individuals in a population

A distribution of sample means consists of:

All possible samples of a given size (N) in a population

What statistics have standard error?

All statistics do, it is the standard deviation of it’s sampling distribution

A sample statistic will never match the population it came from because of ______, and other random samples from the same population because of _______.

Sampling error, sampling variability

Standard error helps us quantify

uncertainty

Margin of Error is:

A quantification of uncertainty, how ‘probable’ scores are to be higher/lower than the point estimate

A 95% Margin of Error is,

a point estimate ±MoE

What is the smallest value of the following for any data set?

Standard Error

CI’s are about _______ errors

managing

The statistic M=3.92, MoE ±3 matches which confidence interval

95% CI [0.92,6.92]

A Confidence Interval expresses

A point estimate and its uncertianty

r=.26 is:

a point estimate

Which of the following is not an assumption required for mean and standard deviation to be powerful

The data must be a normal distribution

Which of the following measures of central tendency captures the least information about a dataset

mode

The mean and mode will be the same for a statistical test if the distribution is:

normally distributed

Tahana computes the variation of her data distribution as 36, what is the standard deviation?

6

Which of the following is true about the standard deviation?

all of the options are true

A regression coefficient indicates

how many units of change in the predicted value of the outcome variable for each unit of change in the predictor variable.

What is the coefficient of determination, or R²

the accuracy of predictions based on the reduction in squared error as a proportion of the total squared error.

A research article compares mean happiness scores across different universities and reports their main statistical finding as "F (2, 36) = 2.95, p = .06." From this information you know that

three groups were compared

A researcher who uses ONLY within-groups designs will NEVER have which of the following problems?

Intelligence as a confounding variable

As sample size increases, the distribution of means

becomes a better approximation of the normal curve

Which of the following research questions would be most appropriate to test using a within-groups experimental design?

Does a 10-minute mindfulness meditation reduce feelings of stress more when compared to a 10-minute casual conversation with a friend?

Which statistical test would be most appropriate to examine the relationship between temperature and number of ice cream cones sold during the month of July?

Pearson correlation

Given the following regression equation on grades and hour’s studying: Ŷ =1.50 + 0.50(X) What grade would a student receive that studied 0 hours?

1.50

Given the following regression equation on grades and hour’s studying: Ŷ =1.50 + 0.50(X) What grade would a student receive that studied 4 hours?

3.5

If we wanted to know what value of y we predict for a given x, what model should we use?

regression

What is the biggest difference between explanatory and predictive regression models?

Explanatory regression models explain data and include error, predictive models do not include error.

b0 is the ____________ and b1 is the____________

regression constant, regression coefficient

Which of the following does NOT describe R²

The general relationship between x and y in a regression model

What is meant by a null hypothesis

a statistical hypothesis of no relationship between groups

Which of the following is a model of a relationship?

all of these

When our data is unlikely enough under a given assumption, we reject that assumption is best characterised as a descriptor of:

The rare event rule in rejecting the null hypothesis

In the rare event rule, how do we quantitatively define a “very unlikely event”?

Our alpha value

What statistical threshold does alpha set in hypothesis testing?

how unlikely something has to be to count as suprising or rare

______ is the threshold of a ‘rare event’, _________ is the probability of data if H₀ is true

alpha, p value

How often is the rare event rule wrong?

about α% of the time (type 1 error)

What is a p-value?

the probability of observing data as extreme as what we have already observed, if H0 was true

about what percent of the time does data fall ±1 SE of the mean?

68%

Finnegan scores z = +1.5 above the mean on a test, what is another way to express this?

+1.5 SE’s above the mean

What is a p value?

the probability of observing data as extreme as we have if H0 is true

Why is a null hypothesis so important?

The most precice statistical prediction we can make is 0

What of the following has the correct order of hypothesis testing?

state the hypothesis, define the comparison, set the decision criterion, compute the test statistic, make a decision

Kiki is setting the threshhold for a rare event in her research under her H0 with an alpha of .05. What step is this of hypothesis testing

Step 3: set decision criterion

Describing the comparison distribution is the distribution of the _________ hypothesis data

null

When defining a comparison distribution, what does this operationally look like?

choosing the correct test to run in jamovi

At what stage of hypothesis testing do we apply the rare event rule to our data?

5.Make a decision

Setting a 1 tailed test means the rare event rule:

applies closer to the mean than a 2 tailed test at about 1.65 SD, in the direction of relationship hypothesised

A research paper rejects the null hypothesis with a sample mean that acheives a z-score of 1.75. Your friend argues this must be incorrect. you:

disagree with them because in a 1 tailed test Zcrit can be set to 1.65 in the direction hypothesised

Retaining the null hypothesis means:

we did not have the statistical power to reject the null hypothesis

If I reject the null hypothesis when the null hypothesis is true, this is:

type 1 error

If I retain H0 when H0 is false, this is:

type 2 error

What is the most reliable way to reduce type 1 error?

decrease alpha value

Which of the following is statistically significant?

p < α

β is often set to .2, what does this mean?

the permissable range for type two error of incorrectly retaining a false null hypothesis

is type 1 or type 2 error typically more likely

type two

what is statistical power?

both of these

If I want to minimise type 2 error, what should I do?

increase α

What is the best way to decrease the spread of the sampling distribution to keep alpha and beta reasonable?

increase sample size

The quantified strength between the variables is:

Effect size

Which of the following does not describe an effect size?

statistical significance (p)

Together, α and p tell us whether an effect is ________, confidence intervals tell us __________.

detectable, the effect size and its precision

Cohens D measures

Effect size with one categorical and one quantitative variable

_______ variables are things our study are not measuring whether they are related or not.

extraneous

control variables are used to

keep noise out of our independant and dependant variable relationship, and attempt to eliminate it as a confound