Statistics Review
Terms
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- Random Sample
- Sample is obtained randomly from the population. Also known as Simple Random Sample.
- Sample
- A sub-collection of elements drawn from the population (size = n)
- Quantitative
- numerical (i.e. SS#, height, weight, temperature, age, score)
- Collectively Exhaustive
- The list of outcomes includes every possible outcome
- Central Tendency
- = expected value OR = average of the discrete distribution
- Box and Whisker Plot (5 summary values)
- Median (Q2), Lower Quartile (Q1), Upper Quartile (Q3), Minimum Value, Maximum Value
- Stratified Sampling
- The population is divided into 2 or more different subpopulations (strata). A random sample is then drawn from each subpopulation. (Male/Female, Undergrad/Grad)
- Nominal Data
- Categories only. Data cannot be arranged in an ordering scheme. (Gender, Race, Religion)
- 4 Conditions of Binomial Probability
- Experiment is classified into one of 2 mutually exclusive categories (success, failure/yes,no); The random variable counts the number of successes in a fixed number of trials; The probability of success/failure stay the same in each trial; The trials are independant of each other.
- Systematic Sampling
- Choose a starting point and then select every n'th element in the population.
- Population
- Complete collection of all elements drawn from the population (size = N)
- Continuity Correction Factor
- Subtract or Add 0.5, depending on the question, to a selected value when a discrete probability distribution is approximated by a continuous probability distribution
- Ratio Data
- Interval data with an absolute 0. Ratios are meaningful. (Length, Width, Weight, Distance)
- Independant Events
- When one outcome does not influence the probability of another outcome. (Coin Toss)
- 2 Fundamental Probability Rules
- The probability, P, of any event occurring is between 0 and 1. The sum of the simple probabilities for all possible outcomes of an activity must = 1.
- Interquartile Range
- The difference between the first and third quartiles
- Frequency Table
- A grouping of qualitative data into mutually exclusive classes showing the number of observations in each class.
- Sampling Distribution
- A sample is simply a portion or part of the population of interest. The resulting sample is then used to estimate population characteristics like mean and variance.
- Sampling with Replacement
- Sampling a group of items of size (n), selecting an item with certain characteristics, replacing it before sampling again. Ensures independance of the elements.
- Contingency Table
- A cross-tabulation table that summarizes 2 variab;es of interest and their relationship.
- Mutually Exhaustive
- Only 1 of the events can occur on any one trial
- Percentiles
- Values of the random variable X that divide a distribution into 100 equal parts (P1,P2....P99) Median is P50.
- Statistics
- Planning experiments, Obtaining data, and Organizing, Summarizing, Presenting, Ananlyzing, Interpreting, and Drawing Conclusions.
- Descriptive Statistics
- Summarize or describe the important characteristics of population data. The goal is to quantitatively describe a population.
- Simple Random Sample
- Representative or porportianate sampling; all members of the population have an equal chance of being sampled, therefore each member should be proportionately represented in the sample. (Z numbers, e-mails)
- Probablility Distribution
- A listing of all of the data values and their associated probabilities
- Cluster Sampling
- Divide the population into categories (clusters) and then randomly select some clusters and sample all members of those clusters.
- Qualitative
- non-numerical (i.e. gender, name, address, race, religion, yes/no)
- Normal Distribution
- Has two parameters (mean, standard deviation); Characteristics include: Bell-shaped curve, Symmetric around the mean, Are under the curve is probability (sum of area = 1)
- Discrete Variables
- Type of ransom variable that can only assume finite or limited set of values (survey questions)
- Decile
- Values of the random variable X that divide the distribution into 10 equal parts (D1, D2.....) Median is D5.
- Sampling without Replacement
- Selecting an item and not returning it to group before re-sampling. N changes upon each sampling.
- Dispersion
- Variance = spread of the data about the mean (expected value)
- Continuous Variables
- Type of random variable that assumes an infinite set of values within a range of values (temp.,sales, time, money)
- Ordinal Data
- Categoried are orderd but differences cannot be determined or they are meaningless. (1st, 2nd, 3rd)
- Data Set
- A set of measurements obtained on some variable
- Conveniance Sampling
- Use results that are already available (phone book, major)
- Relative Frequency
- Captures the relationship between a class total and the total number of observations. = Class total/Grand total
- Quartile
- Values of the random variable X are divided into 4 equal parts (Q1,Q2,Q3,Q4) Median is Q2.
- Interval Data
- Differences between values can be found, but there is no absolute 0. (Temp. and Time)
- Random Variables
- (i.e. XYZ) assigns a real number to the experimental outcome. Each value of the random variable (actual values xyz) has a probability associated with it.