STATS 301 FINAL

What statistical term is this an example of “All CSU students”

population

What statistical term is this an example of “All cars in FOCO”

Population

What statistical term is this an example of “The 113 cars that passed through the intersection that day”

Sample

What statistical term is this an example of “The 372 students measured in the study”

Sample

What statistical term is this an example of “Average stopping distance for all cars in FOCO”

Parameter

What statistical term is this an example of “The average GPA of all CSU students”

Parameter

What statistical term is this an example of “The average GPA of all students in the study”

Statistic

What statistical term is this an example of “The average stopping distance of 6.1 ft”

Statistic

Define Statistical Inference

If we generalize from a sample to a population or using a statistic to inference the value of the parameter

What are quantitative values?

Numeric values.

What are examples of quantitative variables?

Height, weight, number of customers, blood alcohol levels.

What can we do with quantitative variables?

Sensible math.

What must the numbers represent for them to be quantitative variables?

quantities

What are categorical variables?

Names or categories.

Examples of categorical variables

eye color, type of car, political affiliation, breed of dog.

Are non quantitative numbers categorical or quantitative?

Categorical.

Is total points a team scores in a game quantitative or categorical?

Quantitative

Is ZIP code quantitative or categorical?

Categorical

Are predictor variables like the independent or dependent variables?

Independent.

Are response variables like the independent or dependent variables?

dependent

What are predictor variables?

Variables that can predict or explain the response variables

What are response variables?

Variables whose behavior we want to explain; or value we want to predict.

What are confounding variables?

Variables that influence predictor or response but is not accounted for in the study.

What is a confounding variable in simple terms?

A variable that causes the desired response but is not the predictor variable.

What is this an example of, “The number of murders is higher on days when more ice cream is sold”

Confounding variable

What is the difference between observational and experimental studies?

In an experimental study variables are manipulated in an observational study variables are observed

Is a survey an example of an observational or experimental study?

Observational

What does sampling distribution tell us?

The variable a statistic takes on and how often it takes them on

What is a confidence interval?

A range of plausible values for the parameter of interest

How do you create a confidence interval?

Take a point estimate and then adding and subtracting the margin of error.

If our p value is less than .05 can we Reject or FTR our null?

Reject the null

If our p value is greater than .05 can we Reject or FTR our null?

FTR null

If the 95% CI does not contain the null value does this mean we can reject or FTR our null?

Reject Null

If the absolute value of the t-test statistic is greater than 2 do we reject or FTR our null?

Reject null

What range of values is possible for a P value?

Between 0 and 1.

What is the definition of a p value?

The probability that, from a random set of data, you would calculate a t statistic that is at least as large as the one you calculated, if the null hypothesis is true.

What term do we use to describe our result if we reject our null hypothesis?

They are statistically significant

What is Type I error?

Rejecting our null even though it is true

What is Type II error?

Failing to reject our null even though it is false

If our null hypothesis is true even though we rejected it what kind of error could we have made?

Type I

If our null hypothesis is false even though we failed to reject it what kind of error could we have made?

Type II

Equation of what we are testing when it comes to null value

H0 : u1-u2=0

What is one way to reduce Type II errors?

By making the CI narrower to include a smaller range of wrong values

What does lowering alpha do in regards to errors?

It decreases the probability of Type I errors but increases Type II errors and makes it harder to reject Ho

What does shortening the confidence interval do to Beta?

decreases beta

How do we decrease alpha?

Increase the width of the confidence interval by increasing the critical value.

What does shortening the confidence interval do to Alpha?

It increases Alpha

What two things determine Beta?

The effect size and the sample size

What is power defined as?

The statistical probability of not committing a Type II error

What determines power?

Sample Size and Effect Size

What happens to power as sample size increases?

It increases because this makes the confidence interval narrower.

What happens to power as effect size increases?

Power Increases

What happens to effect size as sample size increases?

decreases

This shows a distribution of p values for different values of power. What is a predicted value of power for plot A? Should the value of power for this plot be larger or smaller or in the middle?

.48, middle.

What value of Cohen’s D was used to generate this plot? (0-1)

.5

This shows a distribution of p values for different values of power. What is a predicted value of power for plot B? Should the value of power for this plot be larger or smaller or in the middle?

.051, small.

What value of Cohen’s D was used to generate this plot? (0-1)

.02

This shows a distribution of p values for different values of power. What is a predicted value of power for plot C? Should the value of power for this plot be larger or smaller or in the middle?

.97, large.

What value of Cohen’s D was used to generate this plot? (0-1)

1

This shows a distribution of p values for different values of power. What is a predicted value of power for plot E? Should the value of power for this plot be larger or smaller or in the middle?

.12, small.

What value of Cohen’s D was used to generate this plot? (0-1)

.2

This shows a distribution of p values for different values of power. What is a predicted value of power for plot D? Should the value of power for this plot be larger or smaller or in the middle?

.86, large

What value of Cohen’s D was used to generate this plot? (0-1)

.8

If you collect a sample size that is small will the width of you confidence interval become wider, narrower or stay the same.

If the sample size becomes smaller the width of the CI would become wider.

What is between group variation?

how much the means of the samples vary from one another.

What is within group variation?

how spread out the data are inside each sample.

As sample size decreases, what happens to the degrees of freedom?

Error df decreases and total df decreases

Suppose we hold within-group variation and sample size constant. What happens when we let between-group variation get smaller? Select all that apply.

F-stat gets smaller, R2 gets smaller and P value gets larger

Suppose we hold between-group variation and sample size constant. What happens when we let within-group variation get smaller Select all that apply.

P value gets smaller, F statistic gets larger, R2 gets larger

Suppose we hold between-group variation and within-group variation constant. What happens when we let sample size get smaller? Select all that apply.

F statistic gets smaller, R2 gets smaller, P value gets larger

Does a small or large between group variation result in a small F statistic?

small

Does a small or large within group variation result in a small F statistic?

huge

What combination would give you the smallest R2

small between group variation and huge within group variation.

What happens to p value when F statistic gets larger?

P value gets smaller

What happens to R2 when between group variation gets larger?

R2 gets larger

What happens to MSE when within group variation gets larger?

MSE gets larger

What happens to MSG when between group variation gets larger?

MSG gets larger

What happens to p value when sample size gets larger?

p-value gets smaller

If you have two studies, Study 1 F stat = 5.02, Study 2 F stat = 1.72 which would have a larger MSG/MSE?

Study 1

What is the F statistic?

MSG/MSE

If you have two studies, Study 1 F stat = 5.02, Study 2 F stat = 1.72 which would have a larger p value?

Study 2

If you have two studies, Study 1 F stat = 5.02, Study 2 F stat = 1.72 which would have greater evidence against their null hypothesis?

The second study found weaker evidence against the null hypothesis than the first study found.

How do you write a null hypothesis given 3 samples (use u)

H0: u1=u2=u3

What does anova tell us?

If at least one group mean differs from the others

How do you say in speaking terms a null hypothesis with three different variables regarding the grades example?

The mean grade u1, u2, and u3 are all equal.

Does this box plot show more between group variance or more within group variance?

Between group variance

Does this box plot show more between group variance or more within group variance?

Within group variance

Should a box plot with greater between group variance have overlap?

No boxes should not overlap and be far apart.

Should a box plot with greater within group variance have overlap?

Yes, the boxes should be larger with clear overlap

If your R2 value is .35 what does this tell you about the variation in Holdtimes?

35 % of the variation in HoldTime is explained by differences between the groups.

What is the value of the average between group variation divided by the average within group variation based off of this table?

That is just the F statistic so 8.07

What is the correct statistical decision from this analysis and why?

Reject null hypothesis because the p value is less than .05

In the class notes, we saw an example of performing an ANOVA F-test with data on ectasy use and performance on an abstract reasoning test. There were three groups ecstasy, cannabis and control. After getting the F statistic and p value we rejected the null hypothesis what does this decision suggest about the group population means?

It shows that the population means of at least one of the groups differed from the others.

In the class notes, we saw an example of performing an ANOVA F-test with data on ectasy use and performance on an abstract reasoning test. There were three groups ecstasy, cannabis and control. Write a null hypothesis (=) for this data.

H0: u-ectasy = u-cannabis = ucontrol

How does Y change if X increases if they are correlated

Y will increase

What is the strongest correlation?

The correlation closest to +/- 1

What does r=1 mean?

Perfect correlation

Which is more strongly correlated .8176 or -.8492

\-.8492 because it is closest to -1

What does R =0 mean in terms of correlation?

No correlation

What does |r| > .09 mean about the correlation?

Strong correlation