Old Ones Don't use

Mean and Standard Deviation for Binomial distributions

• np

• √np(1-p)

Mean and Standard Deviation for Geometric distributions

• 1/p

• (√1-p)/p

Proportions One Population Mean and Standard deviation

• √p(1-p)/n

• p

Proportions For two population mean and Standard Deviation

• p₁-p₂

• √p(1-p)/n +√p(1-p)/n

Means for one population standard deviation

• SD/√n

chi-square statistic

(observed-expected)²/expected

The confidence interval for a parameter is of the form _.

point estimate ± margin of error.

A Type I error occurs when the null hypothesis is and is rejected.

true.

To calculate the margin of error, you subtract the from the upper bound of the confidence interval.

point estimate.

The _ tests if the observed counts are consistent with expected counts.

Chi-Square test.

In a ___ random sample, each group of a given size has an equal chance of being chosen.

simple.

The central limit theorem states that when the sample size is sufficiently large, the sampling distribution of the mean will be approximately ___.

normally distributed.

The variable is one that takes on categorical values.

categorical.

The standard deviation gives the typical __ that the values are away from the mean.

distance.

In regression analysis, the ___ measures the strength and direction of the linear relationship between two quantitative variables.

correlation.

___ occurs when the treatment groups are not randomly assigned and thus the explanatory variable cannot be said to have caused the change.

Confounding.

The ___ describes the probability of making a Type II error.

P(Type II error).

The Law of Large Numbers states that simulated probabilities tend to get closer to the true probability as the __ increases.

number of trials.

To ensure the results can be generalized, a sample must be ___ selected.

randomly.

An outlier is any value that falls more than __ above Q3 or below Q1.

1.5 IQR.

When checking the Large Counts condition, use __ when calculating.

p0.

In a matched pairs design, subjects are arranged in __.

pairs.

For a binomial random variable, the number of trials is a __ number.

fixed.

In a double-blind experiment, neither the subjects nor the researchers know which treatment is ___.

administered.

Population

A large group of people or other things

Sample

subset of a population

Statistical Unit

A member of the sample

Population parameter

a number that describes a population

Subject

Human Unit

Observational Study

Statistical Study that observes characteristics or behaviors without changing them

• Survey

Experiment

Assigns Units to different treatments and observes the effects of the treatments

• MUST be random

(blank) is the variable that is adjusted

Explanatory or independent variable

(blank) is what the measured variable is

Dependent or Response variable

(blank) is a variable that is unaccounted for and has an effect on (blank) and (blank)

• Confounding

• explanatory

• Reponse

(blank) accounts for confounding variables so you can infer changes in the (blank) that are due to the explanatory variable

• Control

• Response

(blank) is the group that doesn’t have treatments and it’s purpose is to determine if having a treatment creates new effects

Control Group

(blank) is a variable that is constant to prevent confounding variables

Control Variable

Completely Randomized Design

Units are assigned to treatments at random and are not based on any characteristics

Randomized Block Design

Units with similar characteristics are placed into blocks based on confounding variables and units are assigned treatments at random.

Matched Pair Design

Units with similar characteristics are paired and one unit in each pair is assigned a treatment with the other is the control group

Randomized Design Diagram

Block Design Diagram

Matched Pair Diagram

(blank) is when the subjects don’t know their treatment group and the observers don’t know who belongs in each group

Double Blind Study

(blank) when EITHER the subjects don’t know their treatments OR the observers

Single Blind Study

(blank) has no effect

Placebo

(blank) is a positive or negative trend between two variables

Correlation

(blank) is when changing one variable causes changes in the other

Causation

(blank) can infer causation

(blank) cannot infer causation

• Experiments

• Observation

(blank) is being able to receive consistent results to ensure it is correct

Replication

Law of Large Numbers

Repeating something many times allows it to get closer to the expected results

(blank) observes or samples the entire population

Census

The 5 sampling methods

• Simple Random Sampling

• Systematic Sampling

• Stratified Random Sampling

• Cluster Sampling

• Convenience Sampling

Simple Random Pros and Cons

• Unbiased

• requires all population members

Systematic Pros and Cons

• Unbiased, easier than SRS

• patterns can cause bias

Stratified Pros and Cons

• Addresses all groups (unbiased)

• Needs all population members

Cluster Pros and Cons

• Simple and unbiased

• biased if chosen clusters don’t represent the population

Convenience

• Easiest

• most biased method

Sampling Bias

Not all members are equally likely to be sampled

Undercoverage bias

Not all groups are represented

Response Bias

Not accurate repsonses

Non Response or Voluntary

• Those not responding

• or those who have a strong opinion

Histograms

Probability Density Functions

Dot Plot

Bar Chart

Mosaic Charts

Stem and Leaf Plot

Scatter Plot

Pie Chart

(blank) is the lowest value that excludes outliers

minimum

(blank) is 25% of the data that falls below it or the 25th percentile

Lower Quartile or Q1

(blank) is the 50th percentile

Median

(blank) is the 75th percentile

Upper Quartile or Q3

(blank) is the highest value that excludes outliers

Maximum

IQR

Q3 - Q1

(blank) is a value that differs greatly from other observations

outliers

Lower outlier equation

Q1 - 1.5(IQR)

Upper Outlier equation

Q3 + 1.5(IQR)

(blank) describes a sample while (blank) describes a population

• Descriptive Statistics

• Population Parameters

How to describe a skewed population?

• Minimum

• Q1

• Median

• Q3

• Maximum

• IQR

How to describe a normal population?

• Mean

• Standard deviation

• Variance

• Range

(blank) are countable values

Discrete Variables

(blank) can take on any value in a given range

Continuous Variables

Uniform

Unimodel

Bimodel

Normal Distributions there are (blank)

• 68%

• 95%

• 99.7%

Z score formula

x - mean / standard deviation

How to Describe Distribution

• Shape

• Center

• Variability

• Content

• Comparisons (if possible)

The mean is equal to the (blank)

Percentage

How to calculate if the number of successes is at least ten?

np (trials x percent)

How to calculate if the number of failures is at least ten?

n(1-p)

How to find the standard deviation

How to find the Confidence interval

What are the required conditions for a Confidence Interval?

1. Random Sample or Random Experiment

2. Normality of Sampling Distribution np > 10 and n(1-p) > 10

3. (When without replacement) 10% rule ( n < 0.1N) N=total population

Two ways to Interpret Confidence interval

1. We are C% confident the true proportion of the population is between (point estimate - margin of error) and (point estimate + margin of error)

2. About C% of all samples of the specified size from the population will produce a confidence interval containing the true population proportion

The maximum possible standard deviation is (blank) when (blank)

• √0.25/n

• p = 0.5

Step 1 for Confidence Intervals

• Random Sample

• Normality (np) and (1-(n-p))

• 10% rule (n < 10(N))