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- StudyBlue
- Virginia
- Lord Fairfax Community College
- Statistics

Jennifer S.

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285
Data

Collections of observations (such as measurements, genders, survey responses).

Statistics

The science of planning studies and experiments, obtaining data, and then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions based on the data.

Population

The complete collection of all individuals (scores, people, measurements, and so on) to be studied. The collection is complete in the sense that it includes all of the indivudals to be studied.

Census

The collection of data from every member of the population.

Sample

A subcollection of members selected from a population.

Statistical thinking

Must consider:

Context of the data;

Source of the data;

Sampling method;

Conclusions; and

Practical implications

Key Questions

Guidelines for critically evaluation a statistical study

Some basic principles of ethics

Parameter

Statistic

categorical (or qualitative or attribute) data

Discrete data

continuous (numerical) data

Nominal level of measurement

Ordinal level of measurement

Interval level of measurement

Ratio level of measurement

What is a voluntary response sample?

Why is a voluntary response sample generally not suitable for a statistical study?

What is the difference between statistical significance and practical significance?

Super Bowl: THe New York Giants beat the Denver Broncos in the Super Bowl b a score of 120 to 98.

Thanksgiving: Thanksgiving day will fall on a Monday next year.

Supreme Court: All of the justices on the US Supreme Court have the same birthday.

Lucky Dice: Steve Wynn roled a pair of dice and got a total of 14.

Slot Machine: Wayne Newton hit the jackpot on a slot machine each time in ten consecutive attempts.

Ratio

Interval

Ordinal

Nominal

How do a parameter and a statistic differ?

How do discrete and continuous data differ?

Parameter vs. Statistic

In a large sample of households, the median annual income per household for high school graduates is $19,856 (based on data from the U.S. Census Bureau).

Parameter vs. Statistic

A study of all 2223 passengers aboard the Titanic found that 706 survived when it sank.

Parameter vs. Statistic

If the areas of the 50 states are added and the sum is divided by 50, the result is 196,533 square kilometers.

Parameter vs. Statistic

The author measured the voltage supplied to his home on 40 different days, and the average (mean) value is 123.7 volts.

Discrete or Continuous Data Set

In New York City, there are 3250 walk buttons that pedestrians can press at traffic intersections, and 2500 of them do not work. (based on..._

Discrete or Continuous Data Set

The amount of nicotinein a Marlboro cigarette is 1.2 milligrams.

Discrete or Continuous Data Set

In a test of a method of gender selection developed by the Genetics & IVF Institute, 726 couples used the XSORT method and 668 of them had baby girls.

Discrete or Continuous Data Set

When a Cadillac STS is randomly selected and weighed, it is found to weigh 1827.9 kg.

Nominal, Ordinal, Interval, Ratio

Voltage measurements from the author's home

Nominal, Ordinal, Interval, Ratio

Critic ratings of movies on a scale from 0 star to 4 stars

Nominal, Ordinal, Interval, Ratio

Companies (Disney, MGM, Warner Brothers, Universal, 20th Century Fox) that produced the movies listed in Data Set 7 in Appendix B.

Nominal, Ordinal, Interval, Ratio

Years in which movies were released, as listed in Data Set 9 in Appendix B.

Voluntary response sample (or self-selected sample)

Examples of voluntary response samples which are seriously flawed

Observational Study

Experiment

Simple Random Sample

Random Sample

Probability Sample

Systematic sampling

Convenience sampling

Stratified sampling

Cluster sampling

Cross-sectional study

Retrospective (or case-control) study

Prospective (or longitudinal or cohort) study

Confounding

Important considerations in the design of experiments:

Sampling error

Nonsampling error

Spreadsheet

Excel Worksheet

Center

Variation

Distribution

Outliers

Time

Frequency distribution (or frequency table)

Lower class limits

Upper class limits

Class boundaries

Class midpoints

Class width

Frequency Distribution Procedure

Relative frequency distribution or percentage frequency distribution.

Cumulative frequency

Normal distribution

Histogram

Stemplot

Bar graph

Multiple bar graph

Pareto Chart

Pie chart

Scatterplot (or scatter diagram)

Important principles about graphs

Nonzero axis

Measure of center

Mean (or arithmetic mean)

Median

Mode

Midrange

Round-off rule for the Mean, Median, & Midrange

Skewed

Symmetric

Skewed to the left (negatively skewed)

Skewed to the right (positively skewed)

Range

Round-off rule for measures of variation

Sample Standard Deviation

Population Standard Deviation

Variance

Sample variance

Population variance

Range rule of thumb

Properties of the standard deviation

Empirical Rule for data with a bell-shaped distribution

Coefficient of variation (CV)

Z-score (or standardized value)

Round-off rule for z Scores

Percentiles

Quartiles

Qsub1 (First quartile)

Qsub2 (Second quartile)

Qsub3 (Third quartile)

Interquartile range (IQR)

5-number summary

Boxplot (or box-and-whisker diagram)

False positive

False Negative

True positive

True negative

Measures of test reliability

Rare event rule for inferential statistics

Event

Simple event

Sample space

Relative frequency approximation of probability

Classical approach to probability (requires equally likely outcomes)

Subjective probabilities

Three approaches to finding a probability

Relative frequency approach

Classical approach

Subjective probability

Law of large numbers

The probability of an impossible event

The probability of an event that is certain to occur

For any event A, the probability of A is between 0 and 1 inclusive.

Complement

Rounding off probabilities

Actual odds against event A occurring

Actual odds in favor of event A occurring

The payoff odds against event A occurring

Compound event

Rule for finding the probability that event A occurs or event B occurs.

Formal addition rule

Intuitive addition rule

Disjoint (mutually exclusive)

Rule of complementary events

Multiplication Rule

Conditional probability

Independent/ Dependent events

Formal Multiplication Rule

Intuitive Multiplication Rule

Treating dependent events as independent: The 5% guidleine for cumbersome calculations.

Procedure for finding the probability of at least one of some event

Conditional probability

Intuitive approach to conditional probability

Simulation

Fundamental counting rule

Factorial symbol (!)

Factorial Rule

Permutations Rule (When items are all different)

Permutations Rule (When some items are identical to others)

Combinations rule

Rare event rule for inferential statistics

Random variable

Probability distribution

Discrete random variable

Continuous random variable

Requirements for a probability distribution

Formulas for the

mean,

variance - easier to understand

variance - easier computations

standard deviation

for a probability distribution

Rounding-off rule for mu, sigma, & sigma^{2}

Range rule of thumb:

Rare event rule for inferential statistics

Unusually high number of successes

Unusually low number of successes

Expected value

Binomial probability distribution requirements

Poisson distribution

Requirements for the Poisson Distribution

Parameters of the Poisson Distribution

Differences between Binomial & Poisson Distributions

Requirements for using the Poisson Distribution as an Approximation to the Binomial

Normal distribution

Standard Normal Distribution

Uniform Distribution

Properties of Uniform Distribution

Requirements for a density curve

Standard normal distribution

Table A-2

Procedure for finding a z score from a known area

Critical values

Procedure for Converting from a nonstandard to a standard normal distribution

Procedure for finding values using Table A-2 and the formula

Sampling Distribution of a statistic

The sampling distribution of the mean

Properties of the sampling distribution of the mean

Sampling distribution of the variance

Properties of the sampling distribution of the variance

Sampling distribution of the proportion

Notation for proportions

Properties of the sampling distribution of the proportion

Unbiased estimators

Unbiased estimators

Biased estimators

Central Limit Theorem & the Sampling Distribution of xbar (Givens)

Central Limit Theorem & the Sampling Distribution of xbar (Conclusions)

Central Limit Theorem & the Sampling Distribution of xbar (Practical rules commonly used)

Notation for the Sampling Distribution of xbar

Applying the central limit theorem for an individual value

Applying teh central limit theorem for a sample of values

Finite population correction factor

Normal Distribution as an Approximation to the Binomial Distribution (Requirements)

Normal Distribution as an Approximation to the Binomial Distribution (Normal approximation)

Normal Distribution as an Approximation to the Binomial Distribution (Continuity Correction)

Steps for using the normal distribution to approximate the binomial distribution

Continuity correction

Continuity corrections statements

Using probabilities to determine when results are unusual

Asessing normality

Normal quantile plot (or normal probability plot)

Normal distribution

Not a normal distribution

Point estimate

Confidence interval (or interval estimate)

Confidence level

Critical value

Critical values are based on the following observations

Margin of error

Notation for confidence interval for estimating a population proportion p

Requirements for Confidence intervals

Confidence interval

Procedure for constructing a confidence interval for p

Finding the sample size required to estimate a population proportion Notation

Finding the sample size required to estimate a population proportion Requirements

Finding the Point estimate of p

Finding Margin of Error from a confidence interval

Point estimate

Confidence Interval for Estimating a population Mean (with sigma known) Requirements:

Round-off rule for confidence intervals used to estimate mu

Determining sample size required to _{estimate the population mean mu}

Dealing with unknown sigma when finding sample size

Estimating a population mean: sigma not known

Student t distribution

Degrees of freedom

Finding the confidence interval for estimating a population mean (with sigma not known)

Important properties of the student t distribution

Choosing between z and t

Confidence interval for estimating a population standard deviation or variance

The two main activities of inferential statistics are using sample data to:

Hypothesis

Hypothesis test (or test of significance)

Power

Correlation

Linear correlation coefficient (Pearson product moment correlation coefficient)

Regression equation

Regression line

Marginal change

Influential points

Residual

Least-squares property

Residual plot

Total deviation

Explained deviation

Unexplaned deviation

Coefficient of determination

Predicted interval

Standard error of estimate s_{e}

Multiple regression equation

Adjusted coefficient of determination

Null hypothesis H_{0}

Alternative Hypothesis H_{1} or H_{a}

Type I error in Hypothesis Tests

Type II error in hypothesis tests

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