Statistics-the language of data

Statistic is to data as French is to language of the French.

A solid understanding of statistics provides you with tools to react intelligently to information that you read or hear.

Finally, an important ingredient of a well-executed statistical analysis is to clearly communicate numerical information into written language.

Descriptive statistics refers to the summary of important aspects of a data set. This includes collecting data, organizing the data, and then presenting the data in the forms of charts and tables. In addition, we often calculate numerical measures that summarize, for instance, the data’s typical value and the data’s variability.

Descriptive statistics is summary/describing data. Inferential statistics is drawing conclusions/assumptions.

The phenomenal growth in statistics is mainly in the field called inferential statistics. Generally, inferential statistics refers to drawing conclusions about a large set of data— called a population —based on a smaller set of sample data. A population is defined as all members of a specified group (not necessarily people), whereas a sample is a subset of that particular population. In most statistical applications we must rely on sample data in order to make inferences about various characteristics of the population. For example, a 2010 survey of 1,208 registered voters by a USA TODAY/Gallup Poll found that President Obama’s job performance was viewed favorably by only 41% of those polled, his lowest rating in a USA TODAY/Gallup Poll since he took office in January 2009 (USA TODAY, August 3, 2010). Researchers use this sample result, called a sample statistic, in an attempt to estimate the corresponding unknown population parameter. In this case, the parameter of interest is the percentage of all registered voters that view the president’s job performance favorably. It is generally not feasible to obtain population data and calculate the relevant parameter directly due to prohibitive costs and/or practicality

Population is to population parameter as subset is to sample statistic

Relevant is about what matters and what given information is about.

A population consists of all items of interest in a statistical problem. A sample is a subset of the population. We analyze sample data and calculate a sample statistic to make inferences about the unknown population parameter.

Cross-sectional data contain values of a characteristic of many subjects at the same point or approximately the same point in time. Time series data contain values of a characteristic of a subject over time.

Cross-sectional data is to summer of 2015 as time series data is to holidays of 2015.

When a characteristic of interest differs in kind or degree among various observations, then the characteristic can be termed a variable. We further categorize a variable as either qualitative or quantitative. For a qualitative variable, we use labels or names to identify the distinguishing characteristic of each observation.

Qualitative variable is to labeling as quantitative variable is to analyzing.

A variable that assumes meaningful numerical values is called a quantitative variable. Quantitative variables, in turn, are either discrete or continuous. A discrete variable assumes a countable number of values.

Discrete variables is to specific like 100.2038 as continuous variables is to uncertain like 100-101 or 6'5” as 6'5” instead of 6'5” and 3 cm.

A continuous variable is characterized by uncountable values that are within a certain interval. Weight, height, time, and investment return are all examples of continuous variables. For example, an unlimited number of values occur between the weights of 100 and 101 pounds, such as 100.3, 100.625, 100.8342, and so on. In practice, however, continuous variables may be measured in discrete values. We may report a newborn’s weight (a continuous variable) in discrete terms as 6 pounds 10 ounces and another newborn’s weight in similar discrete terms as 6 pounds 11 ounces.

The nominal scale represents the least sophisticated level of measurement. If we are presented with nominal data, all we can do is categorize or group the data. The values in the data set differ merely by name or label.

With ordinal data we are able to both categorize and rank the data with respect to some characteristic or trait.

Nominal scale is to a unicycle where the wheel is categorization as ordinal scale is to a bicycle where one wheel is categorization and the other wheel is to ranking.

As mentioned earlier, nominal and ordinal scales are used for qualitative variables.

With data on an interval scale, not only can we categorize and rank the data, but we are also assured that the differences between scale values are meaningful. Thus, the arithmetic operations of addition and subtraction are meaningful. The Fahrenheit scale for temperatures is an example of an interval scale. Not only is 60 degrees hotter than 50 degrees, but the same difference of 10 degrees exists as between 90 and 80 degrees Fahrenheit.

Interval scale is to a tricycle where one wheel is categorization, one wheel is ranking, and the other wheel is 'differences between scale values are meaningful' as ratio scales is to a four-wheeler where one wheel is categorization, one wheel is ranking, one wheel is the 'differences between scale values are meaningful', and the last wheel is the 'meaning of zero'.

The importance of a meaningful zero is that ratios can be done. For instance, if a scale is 0-100 and 0 has no meaning 100 could be as bad as it could be good. When zero has a meaning it is easy to see whether 100 is good or bad.

Interval scale can be represented by times. Ratio scales can be represented by money. In these representations, 3:00 p.m. is not necessarily as long as 6:00 p.m. and is not necessarily shorter or longer in length. 3:00 p.m. is 30 minutes after 2:30 p.m. and 6:00 p.m. is 30 minutes after 5:30 p.m. A correlation can be drawn there but 6:00 p.m. and 3:00 p.m. can not be compared as money can. If three adults spend $90 combined on a night out where there were three other adults in the party and those other three adults spend $30 combined then the three adults that spent $90 combined spent a combined total of 3 times what the other three spent combined. In this representation zero has a meaning and a ratio could be built. ($90y$30 30 3). When zero has a value and not an arbitrary one then the comparisons and ratios are more valuable and dependable than when zero is arbitrary. After all when zero's meaning is chosen randomly or on a whim it is like a child that makes a decision to buy candy. It is not responsible and does not benefit anyone or anything else.

Conceptional Review

LO 1.1
Describe the importance of statistics.

A proper understanding of statistical ideas and concepts helps us understand more of the real world around us, including issues in business, finance, health, and social interactions. We must understand statistics or risk making bad decisions and costly mistakes. A knowledge of statistics also provides the necessary tools to differentiate Page 15between sound statistical conclusions and questionable conclusions drawn from an insufficient number of data points, “bad” data points, incomplete data points, or just misinformation.

LO 1.2
Differentiate between descriptive statistics and inferential statistics.

The study of statistics is generally divided into two branches: descriptive statistics and inferential statistics. Descriptive statistics refers to the summary of a data set in the form of tables, graphs, or the calculation of numerical measures. Inferential statistics refers to extracting useful information from a sample to draw conclusions about a population.
A population consists of the complete collection of items with the characteristic we wish to understand. A sample is a subset of the population of interest.

LO 1.3
Explain the need for sampling and discuss various data types.

In general, we use sample data rather than population data for two main reasons: (1) obtaining information on the entire population is expensive and/or (2) it is impossible to examine every item of the population.
Cross-sectional data contain values of a characteristic of many subjects at the same point in time or without regard to differences in time. Time series data contain values of a characteristic of a subject over time.

LO 1.4
Describe variables and various types of measurement scales.

A variable is categorized as either qualitative or quantitative. For a qualitative variable, we use labels or names to identify the distinguishing characteristic of each observation. A quantitative variable assumes meaningful numerical values and can be further categorized as either discrete or continuous. A discrete variable assumes a countable number of values, whereas a continuous variable can take on any value within an interval.
All data measurements can be classified into one of four major categories.
• The nominal scale represents the least sophisticated level of measurement. The values in nominal data differ merely by name or label, and the values are then simply categorized or grouped by name.
• The values of data on an ordinal scale can be categorized and ranked; however, differences between the ranked values are meaningless.
• The interval scale is a stronger measurement scale as compared to nominal and ordinal scales. Values on the interval scale can be categorized and ranked, and differences between scale values are meaningful. The main drawback of the interval scale is that the value of zero is arbitrarily chosen; this implies that ratios constructed from interval-scaled values bear no significance.
• The ratio scale represents the strongest level of measurement. Ratio data have all the characteristics of interval data as well as a true zero point; thus, as its name implies, meaningful ratios can be calculated with values on the ratio scale.
Nominal and ordinal scales are used for qualitative variables. When summarizing the results of qualitative data, we typically count the number or calculate the percentage of persons or objects that fall into each possible category. Interval and ratio scales are used for quantitative variables. Unlike qualitative variables, arithmetic operations are valid on quantitative variables.