Inferential Statistics Fundamentals Flashcards
Define Inferential Statistics
Inferential Statistics allows you to make predictions (“inferences”) from data.
With inferential statistics, you take data from samples and make generalizations about a population.
Inferential statistics rely on what?
Refers to methods that rely on Probability Theory and Distributions to predict population values based on sample data.
What is a Distribution?
A distribution is a function that shows the possible values for a variable and how often they occur.
We usually mean a Probability Distribution. Examples of distributions are:
1. Normal
2. Binomial
3. Uniform - all outcomes have an equal chance of occurring
A distribution is a function that shows the possible values for a variable and the probability of their occurrence.
Shows us the frequency at which possible values occur within an interval
What are Point Estimates?
a single value given as an estimate of a parameter of a population
What are Confidence Intervals?
The range within which you expect the population parameter to be.
It’s estimation is based on the data we have in our sample
A confidence interval is a much more accurate representation of reality
Inferential Statistics are the gateway into…
Fundamentals of Quantitative Research and Data Driven Decision Making
We are sure you have exhausted all possible values when what occurs?
When the sum of the probabilities is equal to 1 or 100%
Is a Distribution just the graph?
No, a distribution is visual representation. It is defined but the underlying probabilities.
What is the relationship of Mean, Median and Mode in a Normal Distribution
They are equal. mean = median = mode. It has no skew.
What is the Origin in a graph?
It is the zero point. Adding it to any graph gives us persepcitve.
Can every distribution be standardized?
Yes
What is Standardization?
Is the process of transforming this variable to a mean of 0 and a stdev of 1
Can a normal distribution be standardized?
Yes, it is called a standard normal distribution
What letter is used to denote a Standard Normal distribution?
Z
What is the standardized variable called?
The z-score. It is equal to the original variable - its mean / its stdev
What are the benefits of using a Standard Normal distribution?
Using it makes predictions and inference much easier.
What is a sampling distribution?
It is a distribution formed my many combined samples
What is Central Limit Theorem?
No matter the underlying distribution, the sampling distribution approximates a normal distribution
For Central Limit Theorem to apply, what is the minimum number of observations?
30
Why is the Central Limit Theorem so important?
CLT allows us to perform tests, solve problems and make inferences using the Normal distribution, even when the population is not normally distributed
What is Standard Error?
is the deviation of the distribution formed by the sample means
Like Stdev the standard error shows variability
What is the formula for Standard Error?
sigma(stdev) / sqrt of n
Why is Standard Error important?
It is used for almost all statistical tests because it shows how well you approximated the true mean
*it decreases as the sample size increases. Bigger samples give a better approximation of the population.
What is an Estimator of a population paramater?
it is an approximation depending solely on sample information. A specific value is called an estimate
What are the two types of Estimates?
- Point Estimates
- Confidence Interval Estimates
What are the differences between Point Estimates and Confidence Intervals?
Point Estimates are a single number - located exactly in the middle of the confidence interval
Confidence intervals are intervals - provide much more information and are preferred when making inferences
What are examples of Point Estimates?
Sample mean x-bar is a point estimate of the population mean mu
What are the two properties of each Point Estimate?
- Bias
- Efficiency
Estimators are like judges, we are always looking for the most efficient and unbiased
An unbiased estimator = has an expected value = the population parameter (example: x-bar = mu)
The most efficient estimators are the ones with the least variability of outcomes. The most efficient estimator is the unbiased estimator with the smallest variance.
What is the difference between Statistics and Estimators?
Statistics is the broader term. A point estimate is a statistic.
You are given a dataset with a sample mean of 10. In this case, 10 is:
a point estimator
or
a point estimate
a point estimate
Example of Sample Mean
The mean salary is $122,150. The sample mean is the estimator and the $122,150 is the estimate.
