# Statistics Terminology

## Terms

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Quantitative
are numerical & can be ordered or ranked. (They all have a certain quantity â€“ age, weight, etc.)
Qualitative
variables that can be placed into distinct categories according to some character or attribute. (They all have a certain quality â€“ all male)
Interval
ranks data and precise differences between units of measure do exist; however, there is no meaningful zero (ex â€“ temperature â€“ no stopping point)
Ration
possesses all characteristics of interval measurement, and there exists a true zero. In addition, true ratio exists when the same variable is measured on two different members of the population.
Nominal
classifies data into mutually exclusive (non-overlapping) exhausting categories in which no order or ranking can be imposed on data. (Ones no more important than the other â€“ names of different characters)
Ordinal
Classifies data into categories that can be ranked; however, precise differences between ranks do not exist. (Small, med, large drinks donâ€™t have to be the same size.)
Stratified
Divide the population into groups according to some important characteristics then sample each group randomly.
Systematic
Randomly assign numbers to subjects and then choose every â€œnthâ€ subject.
Cluster
Start with intact groups to represent the population & then randomly select a few of these groups where all subjects that are members of the selected groups will be involved in the study.
Random
Selected by randomly assigning numbers to subjects & using chance or random methods to choose subjects.
Descriptive
collection, organization, summarization, & presentation of data
Inferential
making generalizations from samples to populations, performing hypothesis testing, determining relationships among variables, & making predictions.
Sample
a measure obtained by using the data values of a sample.
Parameter
A measure obtained by using all the data values for a specific population.
Mean
the sum of the values, divided by the total number of values. The symbol X represents the sample mean.
Median
is the midpoint of the data array. The symbol for median is MD.
Mode
the value that occurs most often in a data set. No symbol.
Range
Highest value & subtract the lowest value. Symbol R is used for range.
Variance
the average of the squares of the distance each value is from the mean.
Standard Deviation
the square root of the variance.
Symettrical (normal curve)
â€“ it is symmetric because itâ€™s a bell shape the highest point is in the center. Itâ€™s evenly distrusted about the mean.
Characteristics of the normal curve
1.The normal distribution curve is bell-shaped

2.The mean, median, & mode are equal and located at the center of the distribution.

3.The normal distribution curve is unimodal (It has only one mode).

4.The curve is symmetric about the mean; shape is the same on both sides of the center.

5.The curve is continuous, that is, there are no gaps or holes.

6.The curve never touches the x axis. Theoretically it only gets increasingly closer.

7.The total area under the normal distr. is equal to 1 or 100%

8.The area under the part of the normal curve that lies within 1 standard deviation is approximately 68%, within 2 standard deviations is 95%, and 3 is 99.7%.
Probability Rules
1.) The probability of any event E is a number (either a fraction or decimal) between and including 0 and 1. Denoted by 0 â‰¤ P (E) â‰¤ 1

2.) If an event E cannot occur (i.e. the event contains no members in the sample space), its probability is 0. (ex if you roll a die there is a 0 probability youâ€™ll get a 9)

3.) If an event E is certain, then the probability of E is 1.

4.) The sum of the possibilities of the outcomes in the sample space is 1.
Probability Experiment
is a chance process that leads to well-defined results called outcomes.
Event
is the set of outcomes of a probability experiment.
Outcome
The result of a single trial.
Permutation
is an arrangement of n objects in a specific order.
Combination
are used when the order or arrangement is not important as in the selecting process. (Ex - pick a committee of 5 students)
Counting Rule
In the sequence of n events in which the first one has k1 possibilities and the second even has k2 and the third has k3 and so forth, the total number of possibilities of the sequence will be
k1 âˆ™ k2 âˆ™ k3 = kn
Hypothesis Testing
a decision-making process for evaluating claims about a population.
How to set up null and alternates
Null (H0) no difference Alternate (H1) is a difference.
H0: M = 25
H1: M â‰  25 or you can use >, <, â‰¤, â‰¥ later two only go on the null! When the problem states less than then the < would go with the alternate. Also need to put a (claim) by whichever we want to find true.
Type I Error
no change in the population, but change in the sample.
Critical Region
is the range of values of the test value that indicate that there is a significant difference and that the null should be rejected.
Corolation
A statistical method used to determine whether a relationship between variables exist.
Regression
A statistical method used to describe the nature of the relationship between variables.
Y = a + bx what does A and B represent?
a is the y-intercept and B is the slope
Correlation Coefficient
computed from the sample data measures the strength and direction of a linear relationship between two variables. Symbol for sample is r. For the population is ρ.
Positive Correlation/relationship
both variables increase and decrease at the same time
Negative correlation/relationship
as one variable increases, the other decreases.
Dependent Variable
The resultant variable.
Independent variable
controlled or manipulated.

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