Stats midterm review

what measure of central tendency is best for an interval or ratio variable?

the mean

What measure of central tendency is best for a nominal variable?

the mode

What measure of central tendency is best for an ordinal variable?

the median

What does interquartile range tell you about the data?

The spread of the data, or, how closely the central values concentrate around the median

what does a box and whisker plot represent?

the extreme values and the interquartile range of a variable

when should you use IQR?

in very skewed data with extreme outliers

when should you use standard deviation?

In more symmetric data with fewer outliers

what are two ways to measure spread?

IQR and standard deviation

How is standard deviation usually expressed?

Alongside the mean: (mean, standard deviation)

What does a density curve tell you?

The overall pattern of how values are distributed across the data

What does a histogram represent?

The frequency of any given value of a quantitative variable

How is a density curve different from a histogram?

A histogram provides the frequency of unique values in a sample; a density curve estimates the distribution of those values within the entire population, based on the sample

How is normal distribution commonly expressed?

~N (mean, standard deviation)

What does a Z score represent?

How many standard deviations a specific value is from the mean (only used if data has normal distribution)

What does a Z score table tell us?

In normal distribution, the percentage of values that lie below a given Z score

How can you find the percentage of data that falls above a certain z score?

Find the probability of the Z score using the Z score table, then subtract that value from 1 and convert your answer to a percentage

What does a negative versus positive z score tell?

A negative z score means that the value of interest lies below the mean, while a positive z score means the value of interest lies above the mean

How do you calculate the percentage of values that lie between two specific values in normal distribution?

1) find the z scores for both values

2) use the z score table to find the probability for both z scores

3) subtract the probability for the lower value from the higher value’s probability

What does it mean if two variables are associated?

Knowing the value of one variable can tell us something about the value of the other variable, but association does not always mean causality

In what ways can association between variables vary?

In direction and strength

What does a scatterplot represent?

The relationship between two quantitative variables whose values are included in each observation; the scatterplot will show the form (shape), strength, and direction of a relationship, as well as any outliers

What does the correlation coefficient represent?

The strength and direction of a linear relationship between two quantitative variables

What are the important properties of the correlation coefficient?

It will always lie between -1 and 1, the direction of the relationship is determined by its sign (+/-), and the closer to 0 the coefficient is, the weaker the relationship

What is a best fit line/regression line?

the line that minimizes the sum of squared differences between the predicted y values and the observed (actual) y values

How do you interpret the regression coefficient?

the expected change in y for each unit increase in x

How do you interpret the regression constant?

The expected value of y if x is 0

What is the difference between correlation and regression?

Correlation measures the strength and direction of a linear relationship, while regression summarizes the relationship between the variables in order to make predictions

What is the model sum of squares (MSS)?

the variation in the outcome that can be explained with the regression line

What is the residual sum of squares (RSS)?

the variation in the outcome that is unexplained (cannot be explained by the regression line)

What does r-squared represent?

the proportion of variation in the dependent variable that can be explained by the regression model; can also be interpreted as the percent of variation in y that is explained by the variation in x

What does it mean when variables are confounding?

their individual effects on an outcome cannot be distinguished from each other

What are the conditions for causation

-theory

-temporal precedence (A must occur before B)

-covariation

-no plausable alternatives

What does a two-way table represent?

the number of cases that fall within each possible pairing in a relationship between two categorical (qualitative) variables

What is internal validity?

whether the independent variable causes the dependent variable in a research design

What is external validity?

How generalizable the findings from a research study are

What is a lurking variable?

A variable not accounted for in a study that may influence the dependent variable

What is a sample space?

Set of all possible outcomes in a probability model

-expressed as S[1,2,3,4]

What does it mean if two events are disjoint?

they cannot occur together in an outcome

What does the mean of a random variable represent?

The expected value of that variable based on all possible values in the sample space and their probabilities