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colorado - Study Guide - Midterm

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STAT EXAM 1 STUDY GUIDE

Key Concepts:

★ Population-

○ The total set of individuals, objects, groups, or events in which the researchers are interested

★ Sample-

○ A number of cases selected from a population

★ Parameter-

○ It can be regarded as a numerical characteristic of a statistical population or a statistical model.

★ Statistic-

○ A set of procedures used by social scientists to organize, summarize, and communicate numerical information

★ Unit of Analysis-

○ The object of research of individual groups, organizations or social artifacts ■ Hypotheses are usually stated in terms of a relationship between independent and dependent variables

★ Level of Measurement-

○ Include: Nominal measurement, Ordinal Measurement, Interval-Ratio Measurement, and Dichotomous Variables

★ Variable-

○ Something that changes

■ Dichotomous variables are a variable that only has two values

■ The Dependent variable is the “effect”

■ Independent variable is the “cause” of the dependent variable

EX) Nominal Variable:

- Using numbers 1 and 2, we can classify female to male

- 1) female 2) male

- Nominal categories cannot be ranked numerically, because the different categories of male and female vary in quality

Variable

Categories

Gender

Female

Male

★ Nominal Measurement-

○ Numbers or other variables are assigned to a set of categories (for the purpose of naming/labeling/classifying observations) We also discuss several other topics like makomé

○ CANNOT be rank-ordered

★ Ordinal Measurement-

○ Numbers are rank-ordered (categories ranging from low to high)

EX) Ordinal Measurement-

- Social class is an example of ordinal measurement

- Upper class, middle class, lower class, working class

- A person in the upper class has a higher position than someone in the middle class R CODE FOR “TAPPLY” FUNCTION WITH CLASSES If you want to learn more check out sw 389 study guide

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★ Interval-ratio measurement-

○ Measurements are expressed in the same units and equally spaces

○ Interval-ratio values can be rank-ordered

★ Frequency Distributions-

○ A table reporting the number of observations that fall into each category of the variable ○ Contrasting a frequency distribution is usually the first step in the statistical analysis of data

★ Measures of Central Tendency-

○ Three types:

■ Mean, median, mode

○ Mode- the category or score with the highest frequency or percentage in the distribution ○ Median- the score that divides the distribution into two equal parts

■ Half the cases are above and half the cases are below

○ Mean- the average of all the total number (arithmetic average)

EX) Mode

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EX) Median

★ How to calculate the mean:

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★ Variance-

○ A measure of variation for interval-ratio and ordinal variables

○ It is the average of the SQUARED deviations from the mean

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★ Standard Deviation-

○ The square root of the variance

★ Skewed Distributions (positive and negative)-

○ Negatively skewed- distribution with a few extremely low values

○ Positively skewed- distribution with extremely high values

R CODE:

- Must install:

- library(psych)

- skew(dats$age)

★ Percentile-

○ A score below which a specific percentage of the distribution falls

★ Interquartile range (IQR)-

○ The width of the middle 50% of the distribution

○ It is defined as the difference between the lower and upper quartiles (Q1 and Q3) ○ IQR can be calculated for interval-ratio and ordinal data

■ Q3= 75%

■ Q1= 25%

○ Quartiles-

■ The median is the second quartile (Q2)

■ The first quartile is the median of the lower half of the observations (Q1)

■ The third quartile is the median of the upper half of the observations (Q3)

★ Pie Chart-

○ A graph showing the differences in frequencies or percentages among the categories of a nominal or an ordinal variable

○ Categories are expressed in a circular graph

★ Bar Graph-

○ A graph showing the differences in frequencies or percentages among the categories of a nominal or an ordinal variable

○ Categories are displayed as rectangles of equal width or their height

★ Histogram-

○ A graph showing the differences in frequencies or percentages among the categories of an interval-ratio variable

○ The categories are displayed as contiguous bars

○ CODE: hist(dats$age)

★ Empirical Rule-

○ The empirical rule states that for a normal distribution, nearly all of the data will fall within three standard deviations of the mean

o 68% of the observations fall within 1 standard deviation of the mean, that is between x-s and x+s (denoted x(-+)s)

o The height corresponds with sometimes the height or number (relative frequency) o 95% of the observations fall within 2 standard deviations of the mean (x+2s) o All or nearly all observations fall within 2 standard deviations of the mean (x+3s)