STAT 120 Quiz 1 and 2

Cases

individuals/objects we obtain information about

• each row of data is representative of a case

Variables

Characteristics measured for each case

Categorical Variables

Each case is placed into one of several groups

Quantitative Variable

Each case is associated w/ a number

Identifier

Something that uniquely characterizes each individual in the dataset.

• An ID number or name

What is a population sample?

A subset of the population

What is statistical inference?

Using data from a sample to gain information about the population

What is an experiment?

Investigate causality by manually manipulating one or more variables.

• researcher manipulates the explanatory variables

What is an observational study?

Exploring associations between variables by observing variables and exploring associations

• researcher does not manipulate any variables

What is a Simple Random Sample?

Each population member is equally likely to be chosen in the sample.

What is an association/ correlation?

Values tend to vary together

• Values of one variable tend to be related to the values of the other variable

What is a causation?

A change in x tends to influence Y.

• If changing the value of one variable influence the value of the other variable

What is a cofounder?

A other variable that causes both X and Y.

• associated with both the explanatory variable and the response variable.

What is an explanatory variable and response variable?

The independent variable. used to predict or explain the values of a response variable.

What is a matched pairs experiment?

Each subject gets both treatments, in a random order?

What is p?

proportion for a population parameter

what is p̂?

p̂ is the proportion of a sample statistic

What is distribution?

The shape of data.

How the data values are centered.

How the data varies.

What are the types of distribution?

What is x̄?

The sample mean/ average

What is μ?

μ is the mean of the population.

What is s?

s is sample standard deviation

what is σ?

σ is the population standard deviation.

What is the equation for standard deviation?

What is the 95% rule?

If a distribution is approximately bell shaped, about 95% of the data should fall within 2 standard deviations of the mean

What is z-score?

The standardized value of a data value x tells us how many standard deviations the value x is above or below the mean

• allows for the comparison of data sets. (should be used for bell-shaped distrubtions)

How to calculate z score?

What is the 5 number summary?

Minimum, Q1, Q2, Q3, Maximum

What is the Interquartile Range (IQR)?

Q3 - Q1

How to read a box plot?

*outliers

IQR outlier test?

lower fence: Q1 - 1.5 (IQR)

upper fence: Q3 + 1.5 (IQR)

How to conduct a graphical summary of a scatterplot?

Form: Linear, Curved, “clumpy”

Direction: Positive, Negative, None, Both

Strength: Amount of variation in y around a trend (weak, strong )

What is r?

the correlation coefficient for the sample

what is ρ?

the correlation coefficient for the population

What is the strength of linear associations?

r = +- 1, strong association

r = 0, weak association

r > 0, positive association

r < 0, negative association

What is linear regression?

Describes a method of modeling y as a linear function of x

What is the least squares method?

A line which minimizes the squared vertical distances between response and the line

What is the equation of a linear regression?

How to interpret the slope of a linear regression?

In context, with units, with direction, say that you are estimating the relationship.

What is a residual?

The difference between the observed and predicted values of the response variables.

• residual = observed - predicted.

What is a residual plot?

Checks a model to see if the association is linear.

If linear, it measures how much variation in the response is explained by the model.

• no pattern indicated a good model fit

What is r-squared?

It measures the proportion of variability observed in the response y, which can be explained by the explanatory variable x.

• correlation coefficient squared in simple linear regression model

How is R² calculated

sd(y)² = variation in y

sd(resid)² = variation from residuals

What is a parameter?

A number that describes some of a population

What is a statistic?

A number that is computed from the data in sample

What is a sampling distribution?

Distribution of the sample statistics computed for different sample of the same size from the same population?

What is the relationship between sample size and standard error?

As sample size increases, the variability (SE) of the sample statistics tends to decrease

What is sample size?

The number of individuals/cases in our sample used to compute the statistic

what is simulation size?

the number of random samples taken from the population to simulate the sampling distribution of our statistic

What is a range of plausible values?

the statistic +- margin of error

What is the margin of error?

The standard error multiplied by a critical value

What is a 95% confidence interval?

If the sampling distribution is relatively symmetric and bell-shaped, a 95% confidence interval can be estimated using

statistic +- 2*SE

What is a confidence interval?

The confidence level tells us what proportion of samples of a given size will give a sample statistic that is within the margin of error of the population parameter

What is the interpretation structure for CI (one parameter)?

I am 95% confident that the population parameter of interest is between # and # units.

What is the interpretation structure for CI (two parameters)?

I am 95% confident that the population parameter 1 of interest in context is between # less/greater and # less/greater units than population parameter 2 of interest in context.

What are common misinterpretation of CI?

Confidence intervals are about populations, NOT samples

Needs context/specificity

The population parameter is in the CI or not, not up to chance

What is a bootstrap sample?

Sample with replacement from the original sample, using the same sample size.

What are bootstrap statistics?

the statistic (mean, avg, proportion, etc) computed from the bootstrap sample.

Bootstrap distribution

the distribution of many bootstrap statistic

What is the percentile method?

If the bootstrap distribution is approximately symmetric, a P% confidence interval equals the percentiles in the bootstrap distribution so that the proportion of the bootstrap statistics between the percentiles equal P%

What is a null hypothesis?

Claim there is no effect or difference. Always about population parameters.

What is the alternative hypothesis?

Claim for which we seek evidence

• always about population parameters