Statistics

Calculating Mean

1. Add up all numbers 2. Divide by how many numbers there are

What is probability of getting a tail when flipping a coin?

1. Calculate Total number of outcomes: There are only two possible outcomes (either heads or tails) = 2 2. How many favorable outcomes are there? When flipping a coin once, there is only one favorable outcome, which is tails = 1 3. Probability = number of favorable outcomes divided by Total number of outcomes, therefore, P = 1/2 = 0.5 or 50%

Calculating Standard Error of the Mean (SEM)

1. Calculate the sample standard deviation 2. Divide by the square root of the sample size

How do I calculate 95% CI using the "Z table"?

1. Convert confidence level of 95% to a decimal = 0.95, and divide by 2 to get 0.475. 2. Search the "Z table" to get the corresponding value that goes with 0.475. You'll see that 0.475 is the intersection of "z = 1.9" on left vertical column and "z + 0.06" in the horizontal row above the table. 3. 95% CI = 1.9 + 0.06 = 1.96

When tossing a coin five times, what is the probability of getting five tails in a row?

1. Each time you toss a coin, there are only two outcomes that you could get (either heads or tails) 2. Since you are tossing the coin five times, you must multiply the number of outcomes per each toss (2) by itself five times (2x2x2x2x2 = 32). Another way to think of this is the result of exponentiation with the number of outcomes per toss (2) as the base, and the total number of tosses (5) as the exponent (i.e. - 2 to the power of 5). 3. There is only one favorable outcome, you must get five tails in a row when flipping a coin five times. 4. Since probability equals the number of favorable outcomes divided by total number of outcomes, then P= 1/32 or 0.03125, 3.125%

Calculating Factorial "!"

1. Factorial Function "!" means to multiply a series of descending natural numbers 2. 4! = 4x3x2x1 = 24 3. 1! = 1 4. 0! = 1

What is the probability of an occurrence of 5 or 6 heads if a coin is tossed ten times?

1. Find the amount of all possible outcomes. We have 10 flips and 2 possible outcomes per flip, which is 2^^10 (exponential) or (2x2x2x2x2x2x2x2x2x2 = 1024). 2. Find possible outcomes with five heads. This is directly done by Combination. Combination = C (n,m), which denotes how many different ways to choose m-sized subsets from an n-sized set (in this scenario m = 5 and n = 10; or C(10,5). 3. C(n,m) = n!/m!/(k)! where "!" is factorial, and k = n-m. In this case, C(10,5) = 10!/5!/(10-5)! = 252. C(10,5) = (10x9x8x7x6x5x4x3x2x1)/(5x4x3x2x1)/(5x4x3x2x1) = 252 4. Now, find possible outcomes with 6 heads. C (10,6) = 10!/6!/(10-6)! = 210. C(10,6) = (10x9x8x7x6x5x4x3x2x1)/(6x5x4x3x2x1)/(4x3x2x1) = 210. 5. Probability equals total number of favorable outcomes divided by Total number of possible outcomes, or P = (252 + 210)/1024 = 0.451 or 45.1%

Calculating Standard Deviation

1. Find the mean set of numbers 2. Subtract the mean from each number in the set 3. Square the answers, then add them together 4. Divide the sum by (n-1) to get the variance (where (n = total set of numbers) 5. Take the square root of the variance

Calculating Variance

1. Find the mean set of numbers 2. Subtract the mean from each number in the set 3. Square the answers, then add them together 4. Divide the sum by (n-1) to get the variance (where n = total set of numbers)

Calculating Probability

1. Probability = Number of favorable outcomes divided by the Total number of outcomes

How is 95% CI calculated in Slide 15 of the "Statistics Introduction" slide deck?

1. Provided data on Slide 15: Sample size (n) = 42; SEM = 1.36; Mean = 40 2. 95% CI = Mean +/- (Z table calculation)*(SEM) 3. 95% CI = 40 +/- (1.96)*(1.36) = 37.33 to 42.67

Standard Deviation

A measure that is used to quantify the amount of variation or dispersion of a set of data values (represented by the Greek letter sigma)

Confidence Interval

A range of scores with specific boundaries (confidence limits) that should contain the population mean. 95% CI (most commonly used) = "95% sure" that the population mean will fall within this CI

Mean

Collection and interpretation of quantitive data and the use of the probability theory to estimate population parameters

Inferential Statistics

Decision making process to estimate "population" characteristics from "sample" data

Calculating 95% CI (Example)

Go to URL (http://www.wikihow.com/Calculate-Confidence-Interval )

Where do I find a "z table"?

Google search "z table Wikipedia" and you will find the table.

Central Limit Theorem (CLT)

If the sample size is large enough (regardless of the population distribution), the sampling means will be normally distributed and the means of all samples will be approximately equal to the mean of the population.

Standard Error of the Mean (SEM)

Is the standard deviation of the sample-mean's estimate of the population mean.

Variance

Measures how far a set of numbers are spread out. A variance of zero indicates that all values are zero

How to calculate a Z score?

Normal/Z Distribution (Standard Normal Distribution is "Bell Curve"

Sampling Error

Sampling error is incurred when the statistical characteristics of a population are estimated from a subset of that population. Since the sample doesn't include all members of the population, statistics on the sample (such as means and quantities) generally differ from statistics of the entire population.

Continuous Sampling

Selection of a series of equal subsets of individuals from within a statistical population to estimate characteristics of the whole population. Each observation measures one or more properties (such as weight, blood pressure, etc.) of observable individuals. By taking equal subsets (of ten for instance) of the population, then taking the mean, you start to get a sense of the properties of the overall population. The more subset samples you take, the better the data reflects the actual entire population of individuals.

Infinite Sampling

The mean/average of all sample means = population mean.

Probability

The measure of the likelihood that an event will occur. Probability is quantified as a number between 0 and 1 (where 0 indicated impossibility and 1 indicates certainty). The higher the probability of an event, the more certain we are that the event will occur.