Math & Statistics Tricks and Definitions

Question 1

Multiplication Trick

Answer 1

If you round one number up, round

the other down to compensate

Question 2

Division Trick

Answer 2

If you round one number up, round

the other up to compensate

Question 3

Logarithmic Identities

Answer 3

log A x B = logA + logB

log A / B = logA - logB

log A^B = B log A

log 1/A = -logA

Question 4

Converting Common and Natrual Logrithms

Answer 4

log x = lnx / 2.303

log (n x 10^m) ~ m + 0.n

Question 5

Scientific Method

Answer 5

Determine whether sufficient background exists

and whether the question is testable

Question 6

FINER Method

Answer 6

Determine whether a study is Feasible, Intersting.

Novel, Ethical, and Relevant

Question 7

Hill’s Criteria

Answer 7

Help determine the strength of causal relationships.

Only temporality is necessary.

Question 8

Small Sample Size

Answer 8

Amplifies the effects of statistical anomalies.

Question 9

Defects in Precision and Accuracy

Answer 9

Create random or systematic variations in the data.

Question 10

Bias

Answer 10

Systematic data error. Common types include selection bias, detection bias,

and the Hawthorne Effect. Minimized by proper participant selection,

blinding, and randomization.

Question 11

Confounding

Answer 11

An analysis error that results when a casual variable is associated with two other variables

in a study but is not accounted for; may falsely indicate that the two variables are associated.

Question 12

Generizability

Answer 12

Statistical significance and casuality do not make something generizable or a good intervention. Clinical significance and the target population must also be considered.

Question 13

Mutually Exclusive

Answer 13

Two events that cannot occur together.

Question 14

Independent

Answer 14

The probability of either event is not affected by the occurrence of the other.

P(A and B) = P(A) x P(B)

P(A or B) = P(A) + P(B) - P(A and B)

Question 15

Null Hypothesis

Answer 15

A hypothesis of no difference; always the comparator.

Question 16

p- value and significance level (α)

Answer 16

The probability that results were obtained by chance given that the null hypothesis is true.

• Compared to the selected significance level (α)- usually 0.05.
• For a directional test, if the p-value is greater than α, then we fail to reject the null hypothesis, which means there’s not a statistically significant difference between the two groups.
• If the p-value is less than α, then we reject the null hypothesis and state that there is a statistically significant difference between the two groups.
• If the alternative hypothesis is not directional, we compare the p-value to α/2 instead. Again, when the null hypothesis is rejected, we state that our results are statistically different.

Question 17

Confidence Interval

Answer 17

A range of values believed to contain the true value with a given level of probability (confidence)

Question 18

Box Plots

Answer 18

Contain information about measures of central tendency and distribution; may be comparative or single.

Also called box-and-whisker: the ends of the whiskers correspond to maximum and minimum value of the data set; outliers can be represented as individual points; the ends of the whiskers correspond to the largest and smallest values in the data that are still within 1.5 x IQR of the median.

Question 19

Standard Deviation (σ)

Answer 19

A measure of how spread out values are from the mean; affected by outliers.

Approximately 68% of data points fall within one standard deviation of the mean, 95% fall within two standard deviations, and 99% fall within three standard deviations.

Question 20

Vector Addition and Subtraction

Answer 20

Question 21

Significance Level α

Answer 21

Set number we compare our p-value to in order to determine rejection or failure to reject hypothesis.

It is the level of risk we are willing to accept for incorrectly rejecting the null hypothesis.

Question 22

Type I Error

Answer 22

Incorrectly rejecting null hypothesis

Question 23

Type II Error (β)

Answer 23

Incorrectly fail to reject the null hypothesis.

In other words, the likelihood that we report no difference between two populations when one actually exists.

Question 24

Power (1 - β)

Answer 24

Probability of correctly rejecting a false null hypothesis (reporting a difference between two populations when one actually exists)

Question 25

Confidence

Answer 25

The probability of correctly failing to reject a true null hypothesis (reporting no difference between two populations when one does not exist)

Question 26

Exponential Graph

Answer 26

Question 27

Logarithmic Graph

Answer 27

Question 28

Median Calculation

Answer 28

(n + 1) / 2

Even numbered data set will provide a noninteger number

Odd numbered data set will provide an integer

Question 29

Skewed Distribution: Negatively Skewed or Positively Skewed

Answer 29

Nonsymmetrical distribution where a tail is seen on one side of the distribution.

Negatively Skewed: tail on the left; mean is lower than median

Positively Skewed: tail on the right; mean is higher than median

Question 30

First Quartile Calculation (Q₁)

Answer 30

• Multiply n by ¼
• If this is a whole number, the quartile is the mean of the value at this position and the next highest position
• If this is a decimal, round up to the next whole number and take that as the quartile position.

Question 31

Third Quartile Calculation (Q₃)

Answer 31

1. Multiply n by ¾
2. If this is a whole number, take the mean of this position and the next.
3. If this is a decimal, round up to the next whole number and take that as the quartile position.

Question 32

Second Quartile (Q₂)

Answer 32

Median of the data set

Question 33

Interquartile range (IQR)

Answer 33

IQR = Q₃ - Q₂

Can be used to determine outliers- any value that falls more than 1.5 interquartile ranges below the first quartile or above the third quartile is considered an outlier.

Question 34

Outlier Calculation

Answer 34

1.5 x IQR below Q₁ or 1.5 x IQR above Q₃

Question 35

Accuracy

Answer 35

Also called validity; the quality of approximating the true value

Question 36

Precision

Answer 36

Also called reliability; the quality of being consistent in approximations

Question 37

Hawthorne Effect

Answer 37

Results from changes in behavior- by the subject, experimenter, or both- that occur as a result of the knowledge that the subject is being observed