Ch 12 - Data Based and Statistical Reasoning

Question 1

What does measure of central tendency provide?

Answer 1

a single value representation for the middle of a group of data

Question 2

What is the arithmetic mean (average)?

Answer 2

a measure of central tendency that equally weighs all values; it is not affected by outliers

Question 3

What is the median?

Answer 3

the value that lies in the middle of the data set
- 50% of data points are above and below the median.
(n+1)/2 where n is the number of data values

Question 4

What is the mode?

Answer 4

the data point that appears most often; there may be multiple (or 0) modes in a data set

Question 5

What is normal distribution?

Answer 5

symmetrical; the mean, median, and mode are all the same

Question 6

What is standard distribution?

Answer 6

a normal distribution with a mean of 0 and a standard deviation of one

• used for most calculation
• 68% of data points occur within one standard deviation of the mean, 95% within 2, and 99% within 3

Question 7

What are skewed distributions?

Answer 7

have differences in their mean, median, and mode

- the skew direction is the direction of the tail of the distributions

Question 8

What are bimodal distributions?

Answer 8

have multiple peaks, although not necessarily multiples modes
- may be useful to perform data analysis on the 2 groups separately

Question 9

What is range?

Answer 9

the difference between the largest and smallest values in a data set

Question 10

What is interquartile range?

Answer 10

difference between the value of the 3rd quartile and the 1st quartile (IQR = Q3 - Q1)
- can be used to determine outliers
Q1 = n x 1/4
Q3 = n x 3/4
(if whole, take mean of this position and next, if decimal round up to the next whole number and take that as quartile position)

Question 11

What is standard deviation?

Answer 11

a measurement of variability about the mean
- can also be used to determine outliers
sigma = square root (sum (value - mean)^2)n-1

Question 12

What are outliers?

Answer 12

may be a result of true population variability, measurement error, or a non normal distribution

• any value lower than 1.5 x IQR below Q1 or any value higher than 1.5 x IQR above Q3
• any value that lies more than 3 standard deviations from the mean

Question 13

What are independent and dependent events?

Answer 13

• the probability of independent events does not change based on the outcome of other events
• the probability of dependent events changes depending on the outcome of other events

Question 14

What are mutually exclusive outcomes?

Answer 14

cannot occur simultaneously

Question 15

What does it mean for a set of outcomes to be exhaustive?

Answer 15

there are no other possible outcomes

Question 16

How are hypothesis tests used?

Answer 16

use a known distribution to determine whether a hypothesis of no difference (the null hypothesis) can be rejected

Question 17

What does the p value determine?

Answer 17

whether or not a finding is statistically significant is determined by the comparison of a p value to the selected significance level
- significance level 0.05 is commonly used

Question 18

How do the mean, median, and mode compare for a right-skewed distribution?

Answer 18

the mean of a right (positively) skewed distribution is to the right of the median, which is to the right of the mide

Question 19

How do range and standard deviation generally relate to one another mathematically?

Answer 19

where the data are not available, the range can be approximated as 4x the standard deviation

Question 20

Why would the average difference from the mean be an inappropriate measure of distribution?

Answer 20

• the average distance from the mean will always be 0, which is why we always square the distance from the mean and then take the square root at the end for standard deviation
• it forces all of the values to be positive numbers, which will not cancel out to 0

Question 21

What are the probability rules?

Answer 21

• and: multiply the probabilities

- or: add the probabilities (and subtract the probability of both happening together)

Question 22

What are confidence intervals?

Answer 22

used to determine a potential range of values for the true mean of a population

Question 23

How is the p value calculated during a hypothesis test?

Answer 23

after the test statistic is calculated, a computer program or table is consulted to determine the p value of the statistic

Question 24

How is power related to probability?

Answer 24

power is the probability that the individual rejects the null hypothesis when the alternative hypothesis is true for the population

Question 25

How do exponential and parabolic curves differ in shape?

Answer 25

they both have a steep component; however, exponential have horizontal asymptotes and become flat on one side while parabolic are symmetrical and have steep components on both sides of a center point

Question 26

What is correlation?

Answer 26

refers to a connection - direction relationship, inverse relationship, or otherwise - between data

Question 27

What is causation?

Answer 27

correlation does not necessarily imply causation, but causation does mean correlation

Question 28

What is required in order for a conclusion to be useful?

Answer 28

there must be practical (clinical) and statistical significance

Question 29

What is a type 1 error?

Answer 29

the probability of mistakenly rejecting the null hypothesis

• set by selecting a significant level
• p value is greater than significance level

Question 30

How is the confidence level increased?

Answer 30

to increase the confidence level, one must increase the size of the confidence interval to make it more likely that the true value of the mean is within the range
- thus making the confidence interval wider

Question 31

What is the most common measure of distribution?

Answer 31

standard deviation; it is most closely linked to the mean of a distribution and can be used to calculate p values, which are probabilities