ISDS Chapter 1
The Nominal Scale
- The least sophisticated level of measurement. - Data are simply categories for grouping the data.
The Interval Scale
- Consider the Fahrenheit scale of temperature. - This scale is _____ because the data are ranked and differences (+ or ) may be obtained. But there is no "absolute 0" (What does 0F mean?)
The Interval Scale
- Data may be categorized and ranked with respect to some characteristic or trait. - Differences between interval values are equal and meaningful. - No "absolute 0" or starting point defined. Meaningful ratios may not be obtained.
The Ordinal Scale
- Differences between categories are meaningless because the actual numbers used may be arbitrary. - There is no objective way to interpret the difference between instructor quality.
To do good statistics, you must
- Find the right data. - Use the appropriate statistical tools. - Clearly communicate the numerical information into written language.
Statistics
- Language of data - Study of collecting, analyzing, presenting, and interpreting data - Science of getting useful information from data
Cross- Sectional Data
- Many subjects at same point in time - Without regard to differences in time * Individuals, households, firms, countries
Discrete Quantitative (Numerical) Variables
- Number of children in a family - Number of points scored in a basketball game. - Number of books purchased - Number of classes taken
Time Series Data
- One subject over several time periods - Daily, weekly, monthly, quarterly, annual * Monthly sales, daily price, weekly rate
The Ratio Scale
- The strongest level of measurement. - Ratio data may be categorized and ranked with respect to some characteristic or trait. - Differences between interval values are equal and meaningful. - There is an "absolute 0" or defined starting point. "0" does mean "the absence of ..." Thus, meaningful ratios may be obtained.
Reasons for sampling from the population
- Too expensive to gather information on the entire population - Often impossible to gather information on the entire population
Continuous Quantitative (Numerical) Variables
- Weight - Height - Investment return - Length of time
Qualitative (Categorical) Variables
- Yes/No - Day of Week - Year Classification - Name of Insurance Provider
Descriptive and Inferential
2 Branches of statistice
Sample
A subset of the population.
Nominal, Ordinal, Interval, Ratio
All data measurements can be classified into one of four major categories
Discrete Quantitative (Numerical) Variables
Countable number of distinct values
Continuous Variable
Can take on any value within an interval. Using a sufficient precision of measurement, no two continuous values are identical.
Nominal
Categorical data; data in each group differ by name or label
Descriptive
Characterize data i.e., the sample mean
Descriptive Statistics
Collecting, organizing, and presenting the data.
Population
Consists of all items of interest.
Parameter
Described characteristic of a population - P & P
Statistic
Describes characteristic of a sample - S & S
Quantitative (Numerical) Variables
Discrete and Continuous
Zero Point
Does not reflect a complete absence of what is being measured
Inferential Statistics
Drawing conclusions about a population based on sample data from that population.
Correlation- to- Causation
Even if two variables are highly correlated, one does not necessarily cause the other.
Ordinal Scale
Example: instructors are often evaluated on an ordinal scale (excellent, good, fair, poor).
Values
Expressed in words but coded into numbers for processing purposes
Problem with Conclusion
Incorrect to draw conclusion based on one data point.
Continuous Quantitative (Numerical) Variables
Infinite number of values within some interval
Quantitative Variables
Interval and Ratio
Interval Scale
Is used with Quantitative variables
Arbitrarily Chosen
Main drawback is the value of zero is ______
Qualitative Values
May be converted to quantitative values for analysis purposes.
Descriptive
Methods to help collect, summarize, and analyze set of data. Use when you know all of the data points
Inferential
Methods use data collected from a small population to make inferences, draw conclusions, about a larger population.
Qualitative Variables
Nominal and Ordinal
Scales of Meausure
Nominal and Ordinal > Qualitative Variables Interval and Ratio > Quantitative Variables
Parameter
Numerical measure that describes a characteristic of a population.
Staristic
Numerical measure that describes a characteristic of a sample.
Ordinal Scale
Ordinal data may be categorized and ranked with respect to some characteristic or trait.
Discrete Variable
Takes on individually distinct values.
The Ratio Scale
The following variables are measured on a ratio scale: - General Examples: Weight, Time, and Distance - Business Examples: Sales, Profits, and Inventory Levels
Variable
The general characteristic being observed on an object of interest
Statistics
The methodology of extracting useful information from a data set
Qualitative
Unlike ______ data, arithmetic operations are valid on interval and ratio scaled data.
Inferential
Use when the actual count is not easily obtainable. Often times inferences are made about college students based on data obtained in a sample.
Summarizing
When __________ typically count number or calculate the percentage of persons or objects that fall into each possible category.
Importance of Statistics
With knowledge of statistics: - Avoid risk of making uninformed decisions and costly mistakes - Differentiate between sound statistical conclusions and questionable conclusions.
