Basic statistical concepts: Data collection by sampling method

Data sampling is used to learn more about people such as consumers, events such as consumer spending, and information such as how much a consumer spends. In other words, data sampling is the acquisition of recorded numbers, information, facts or events in the form of a data set or multiple data sets. This data set is the data sample that is used in obtaining statistical answers for questions. 

Data can be collected in a number of ways, one of which is the sample method. Other methods of data collection include data mining, aggregate data gathering, random sampling, and qualitative research. This article will discuss data collection by sampling in terms of 1) its objectives, 2) how it can be done and 3) how it is analyzed.

Objectives of data sampling collection

Data sampling attempts to achieve some core objectives relevant to the statistical study in question. Specifically, sample data is utilized in a number of disciplines/fields to learn more about the subject. Moreover, in marketing, sample data may be used to learn more about people's behavior, choices, and actions for the purpose of improving marketing techniques and goals. The points listed below indicate some of the ways sample data can be used to determine.

• Information about a larger sample or population group

• Relationships between events, things or actions with other things, events or actions

• Identification of trends and patterns

• Grouping of sample data for categorization

• Analysis for research evidence and/or verification 

• Functionality of software analysis tools

An illustration of data sampling

Data sampling can be analyzed and implemented in a number of ways as we have seen. However, how this is done can vary so an illustration of how sample data is gathered and studied can be helpful. In the following hypothetical example, 1000 people are asked to partake in a statistical study. The study attempts to achieve market research into the juice flavor preferences of the 1000 people who are of different ages, gender and cultural background. To do this the following steps are taken:

• Create a simple survey with a few questions that can be used in the sample analysis

• Locate a suitable population sample from which to gather the data

• Of that population recruit 1000 of them to participate in the survey study

• Perform the research by having the population sample fill out the survey

• Analyze the data using statistical tools, software and/or techniques

• Draw conclusions based on the evidence presented by the sampling data

To further illustrate, data sampling helps answer questions like the following example: If 1000 people drink juice every day and have a choice of apple, tomato and grape juice what will be the affect on that sample population if orange juice is added to the selection? In this example, the dependent variable is the numbers of people selecting each type of juice, for example 700 apple, 100 tomato and 200 grape. The independent variable is the orange juice. The data sample is the number of people who drink each type of juice after the addition of orange juice.

Analysis of sample data

To further illustrate data sampling, data sets are used in statistics to deduce statistical relationships and characteristics of the sample data set and between independent and dependent variables within the sample data alone. Dependent variables are the individual records within a data set that are influenced by a change in the dependent variable. Sample data can be acquired a number of ways for example by primary or secondary research. The application and analysis of sample data can be used in many ways, some examples being double blind studies, control experiments, population surveys, hypothesis testing and more.

In the above example sample study of juice drinkers the affect of introducing orange juice to their choice of juices is the sample data. The data was collected with surveys rather than by observation(s), and the study was at one fixed point in time and not a over time. Thus, studies can be limited or extensive depending on what sample data is collected and how it is analyzed. How data is gathered and an analyzed can thus have a decidedly significant affect on the quality of the data and the extent of its use.

For example, the data can be analyzed simply for summary statistics such as X amount of people would drink orange juice if the given the choice out of 4 juices and Y amount of people would drink grape juice. However, the data can be further analyzed for accuracy using regression analysis in which alpha, beta and P-values are determined to aid in determining the validity of the statistics garnered through the sample data. These values help determine correlation, falsification due to pre-existing beliefs being tested, and probability of accuracy. Another way the information can be used is in cluster analysis in which the patterns of information are grouped for the purpose of assessing additional relationships. For example, the number of grape juice drinkers who would choose orange juice if grape juice were not available.

Sources:

1. http://home.ubalt.edu/ntsbarsh/Business-stat/opre504.htm#rrTopiinbuSt
2. http://brent.tvu.ac.uk/dissguide/hm1u3/hm1u3text3.htm
3. http://www.businessdictionary.com/
4. http://www.investorwords.com/
5. http://dictionary.babylon.com/

The Use of Normal Distribution in Finance

A financial normal distribution is a statistical term used to describe how particular population sample characteristics or event(s) results are placed in relation to each other. The normal distribution is used to help predict and adjust for a wide range of financial goals by optimizing financial decision-making by applying and graphically mapping financial data into a distribution set of variables.

In other words, data such as prices can be plotted on a normal distribution graph with dots. The dots are then connected with a line that reveals the data's distribution in terms of two axis continuums known as the X and Y axis on a graph. An example of a normal distribution is the amount of money spent on obtaining the calories consumed by individuals over time. If the X axis represents calories consumed, and the Y axis represents cost per calorie, the data set will produce a statistical and graphical distribution when plotted on graph.

This article will illustrate how the normal distribution is used in finance in addition to providing tips and techniques for applying the normal distribution to financial practices such as investing. It is important to note the normal distribution is not the only type of statistical distribution, and thus the mathematical benefits arising from use of normal distributions in finance may not be realized for non-normally distributed data.

How normal distribution is used in finance

The normal distribution is used to make quantitative and qualitative financial decisions based on the mathematical nature of normal distributions. This is to say, normal distributions tend to follow certain similarities such as conglomeration of distribution toward the mean among other things such as standard deviation from the mean.

Due to this and other trends, numerical forecasting is more justified by the statistical patterns underlying the data. Thus, determining if certain financial events are normally distributed can be useful because those events may be more likely to follow probabilistic patterns in the future.

To illustrate further, the normal distribution helps financial analysts and/or investors make better financial decisions based on the statistical information provided by the normal distribution. Using the example above, if a sample of 20,000 people reveals that the average daily calorie consumption of Americans is 2100 calories per day, and the majority of food consumers are near this range, with others calorie levels tapering off evenly above and below this point, the distribution is normal.

This can then lead to a mathematical connection between calories consumed and dollars spent on calories. The data can be further analyzed if two normal distributions exist at different price levels all other variables such as population held constant.

If investors want to determine how caloric intake affects consumption trends at fast food chains, it is probable a maximum revenue for the chain can be assumed based on the normal distribution of the population samples caloric intake. Furthermore, if price per calorie rises at the fast food chain, a new normal distribution may be formed creating what is known as correlation or the statistical measurement of a change in one set of variables influencing another set of variables.

For example, if the price of burgers at a burger food chain rise by 20% and the caloric intake of the population declines but is still normally distributed, a correlation may be present. The degree of these correlations can be used to determine if price rises may be profitable and therefore a good or bad investment. A few more ways normal distributions can be used in finance are listed below.

• To determine probability of financial events occurring 

• Can be used in comparing financial events and/or products 

• Statistically assists in assessing risk 

• Helps in forecasting return on investment (ROI) 

• Presents data in an easier to understand format 

• Allows an investor to measure statistical accuracy 

Tips and techniques for applying normal distributions

When using normal distributions to make financial decisions, there are techniques and rules that can be utilized to make the abstract nature of statistics more down to earth and 'realistic' in terms of common financial concerns such as profit, cost, accuracy of information, competitiveness etc. A few of these rules and principles are listed below and may convey a more helpful way to make sense of and apply normal distributions in finance.

• Determine the line of best fit: When multiple data sets are obtained from the same sample group over time, an average distribution can be obtained. This is known as the line of best fit, which if a group of normal distributions without a change in variables, has the effect of averaging the normal distribution. Thus, a normal distribution that is averaged in this way may be more accurate.

• Find the Beta value: The beta value is the correlation i.e. relationship between a depending variable such as a company stock price with an independent variable such as industry raw materials costs. If the beta value is above 1, the correlation of movements in prices between the two variables is higher.

• Look at the P-Value: When comparing two hypotheses represented by normal distributions the P-value illustrates the quality and strength of the statistical analysis. Small P-values under .05 or lower are good.

• Use computer software: A good statistical software program will make the tough statistical calculations easy with a sound understanding of the statistical principles and their application in finance. This saves time and energy on calculations.

• Make sure the distributions are relevant: Normal distributions may not be financially helpful if they don't have a strong bearing and implication on a financial decision being made. For this reason, making sure the information is relevant can help optimize decision-making.

• Plot the distribution on a graph: Graphical illustrations of statistical data can help make it more understandable and complement statistical values and probabilities.

Summary

Normal distributions help determine financial trends and relationships. These trends and relationships can then be used for comparing financial products, forecasting financial outcomes, assessing risk, and predicting return on investment, estimating cost and demand among other things.

Certain statistical data may be more useful than other statistical data so it is important to know what to look for when applying the statistical values of normal distributions to financial evaluations and choices. Also, since not all distributions are normal, it is important to determine whether or not a distribution is in fact normal, for the mathematical characteristics of normal distributions to apply. When utilizing normal distributions correctly applying the data derived from the distribution to the financial application is key.

Sources:

1. http://tinyurl.com/4s77kpt
2. http://www.investopedia.com/terms/n/normaldistribution.asp
3. http://www.investorwords.com/3344/normal_distribution.html
4. http://www.childrensmercy.org/stats/definitions/pvalue.htm
5. http://www.netmba.com/statistics/distribution/normal/