In Module Seven, you will submit your selection of statistical tools and data an

Question

In Module Seven, you will submit your selection of statistical tools and data analysis, which are critical elements III and IV. You will submit a 3- to 4-page paper and a spreadsheet that provides justification for the appropriate statistical tools needed to analyze the company’s data, a hypothesis, the results of your analysis, any inferences from your hypothesis test, and a forecasting model that addresses the company’s problem. Specifically, the following critical elements must be addressed: III. Identify statistical tools and methods to collect data: A. Identify the appropriate family of statistical tools that you will use to perform your analysis. What are your statistical assumptions concerning the data that led you to selecting this family of tools? In other words, why did you select this family of tools for statistical analysis? B. Determine the category of the provided data in the given case study. Be sure to justify why the data fits into this category type. What is the relationship between the type of data and the tools? C. From the identified family of statistical tools, select the most appropriate tool(s) for analyzing the data provided in the given case study. D. Justify why you chose this tool to analyze the data. Be sure to include how this tool will help predict the use of the data in driving decisions. E. Describe the quantitative method that will best inform data-driven decisions. Be sure to include how this method will point out the relationships between the data. How will this method allow for the most reliable data? IV. Analyze data to determine the appropriate decision for the identified problem: A. Outline the process needed to utilize your statistical analysis to reach a decision regarding the given problem. B. Explain how following this process leads to valid, data-driven decisions. In other words, why is following your outlined process important? C. After analyzing the data sets in the case study, describe the reliability of the results. Be sure to include how you know whether the results are reliable. D. Illustrate a data-driven decision that addresses the given problem. How does your decision address the given problem? How will it result in operational improvement?

Explanation / Answer

(A) Identify the appropriate family of statistical tools that you will use to perform your analysis

Statistical Analysis Tools are required for a thorough and scientifically valid analysis of survey results. There are several choices available for the researcher to choose from – ranging from the simple tools available with all survey packages that calculate percentages and totals

1. Mean

The arithmetic mean, more commonly known as “the average,” is the sum of a list of numbers divided by the number of items on the list. The mean is useful in determining the overall trend of a data set or providing a rapid snapshot of your data. Another advantage of the mean is that it’s very easy and quick to calculate.

2. Standard Deviation

The standard deviation, often represented with the Greek letter sigma, is the measure of a spread of data around the mean. A high standard deviation signifies that data is spread more widely from the mean, where a low standard deviation signals that more data align with the mean. In a portfolio of data analysis methods, the standard deviation is useful for quickly determining dispersion of data points.

3. Regression

Regression models the relationships between dependent and explanatory variables, which are usually charted on a scatterplot. The regression line also designates whether those relationships are strong or weak. Regression is commonly taught in high school or college statistics courses with applications for science or business in determining trends over time.

4. Sample Size Determination

When measuring a large data set or population, like a workforce, you don’t always need to collect information from every member of that population – a sample does the job just as well. The trick is to determine the right size for a sample to be accurate. Using proportion and standard deviation methods, you are able to accurately determine the right sample size you need to make your data collection statistically significant.

5. Hypothesis Testing

Also commonly called t testing, hypothesis testing assesses if a certain premise is actually true for your data set or population. In data analysis and statistics, you consider the result of a hypothesis test statistically significant if the results couldn’t have happened by random chance. Hypothesis tests are used in everything from science and research to business and economic

Numerical data. These data have meaning as a measurement, such as a person’s height, weight, IQ, or blood pressure; or they’re a count, such as the number of stock shares a person owns, how many teeth a dog has, or how many pages you can read of your favorite book before you fall asleep. (Statisticians also call numerical data quantitative data.)

Categorical data: Categorical data represent characteristics such as a person’s gender, marital status, hometown, or the types of movies they like. Categorical data can take on numerical values (such as “1” indicating male and “2” indicating female), but those numbers don’t have mathematical meaning. You couldn’t add them together, for example. (Other names for categorical data are qualitative data, or Yes/No data.)

Qualitative data

Qualitative data is a categorical measurement expressed not in terms of numbers, but rather by means of a natural language description. In statistics, it is often used interchangeably with "categorical" data.

Quantitative data

Quantitative data is a numerical measurement expressed not by means of a natural language description, but rather in terms of numbers. However, not all numbers are continuous and measurable. For example, the social security number is a number, but not something that one can add or subtract.

(C) Describe the quantitative method

Quantitative research — including surveys and customer questionnaires — can help small firms to improve their products and services by enabling them to make informed decisions

Quantitative research is about asking people for their opinions in a structured way so that you can produce hard facts and statistics to guide you. To get reliable statistical results, it’s important to survey people in fairly large numbers and to make sure they are a representative sample of your target market.

What can quantitative research tell you?

Is there a market for your products and services?

What awareness is there of your product or service?

How many people are interested in buying your product or service?

What type of people are your best customers?

What are their buying habits?

How are the needs of your target market changing?

Analysing the results of your quantitative research

Collecting data is just one part of the research task. You have to collate it and analyse it as well. With a complex survey, this can be a specialist task in order to extrapolate all the findings and drill down into the data to see how different groups have responded. However, a simple survey can be very effective and highly revealing and small firms can always benefit from asking their customers what they think

Time-series: A single variable is captured over a period of time, such as the unemployment rate over a 10-year period. A line chart may be used to demonstrate the trend.

Ranking: Categorical subdivisions are ranked in ascending or descending order, such as a ranking of sales performance (the measure) by sales persons (the category, with each sales person a categorical subdivision) during a single period. A bar chart may be used to show the comparison across the sales persons.

Part-to-whole: Categorical subdivisions are measured as a ratio to the whole (i.e., a percentage out of 100%). A pie chart or bar chart can show the comparison of ratios, such as the market share represented by competitors in a market.

Deviation: Categorical subdivisions are compared against a reference, such as a comparison of actual vs. budget expenses for several departments of a business for a given time period. A bar chart can show comparison of the actual versus the reference amount.

Frequency distribution: Shows the number of observations of a particular variable for given interval, such as the number of years in which the stock market return is between intervals such as 0-10%, 11-20%, etc. A histogram, a type of bar chart, may be used for this analysis.

Correlation: Comparison between observations represented by two variables (X,Y) to determine if they tend to move in the same or opposite directions. For example, plotting unemployment (X) and inflation (Y) for a sample of months. Ascatter plot is typically used for this message.

Nominal comparison: Comparing categorical subdivisions in no particular order, such as the sales volume by product code. A bar chart may be used for this comparison.

Geographic or geospatial: Comparison of a variable across a map or layout, such as the unemployment rate by state or the number of persons on the various floors of a building. A cartogram is a typical graphic used.

Techniques for analyzing quantitative data

Check raw data for anomalies prior to performing your analysis;

Re-perform important calculations, such as verifying columns of data that are formula driven;

Confirm main totals are the sum of subtotals;

Check relationships between numbers that should be related in a predictable way, such as ratios over time;

Normalize numbers to make comparisons easier, such as analyzing amounts per person or relative to GDP or as an index value relative to a base year;

Initial data analysis

The most important distinction between the initial data analysis phase and the main analysis phase, is that during initial data analysis one refrains from any analysis that is aimed at answering the original research question. The initial data analysis phase is guided by the following four questions

Quality of data

The quality of the data should be checked as early as possible. Data quality can be assessed in several ways, using different types of analysis: frequency counts, descriptive statistics (mean, standard deviation, median), normality (skewness, kurtosis, frequency histograms, n: variables are compared with coding schemes of variables external to the data set, and possibly corrected if coding schemes are not comparable.

Test for common-method variance.

The choice of analyses to assess the data quality during the initial data analysis phase depends on the analyses that will be conducted in the main analysis phase.

Quality of measurements

The quality of the measurement instruments should only be checked during the initial data analysis phase when this is not the focus or research question of the study. One should check whether structure of measurement instruments corresponds to structure reported in the literature.
There are two ways to assess measurement

Analysis of homogeneity (internal consistency), which gives an indication of the reliability of a measurement instrument. During this analysis, one inspects the variances of the items and the scales, the Cronbach's of the scales, and the change in the Cronbach's alpha when an item would be deleted from a scale.

Initial transformations

After assessing the quality of the data and of the measurements, one might decide to impute missing data, or to perform initial transformations of one or more variables, although this can also be done during the main analysis phase.
Possible transformations of variables are:

Square root transformation (if the distribution differs moderately from normal)

Log-transformation (if the distribution differs substantially from normal)

Inverse transformation (if the distribution differs severely from normal)

Make categorical (ordinal / dichotomous) (if the distribution differs severely from normal, and no transformations help)

Did the implementation of the study fulfill the intentions of the research design?

One should check the success of the randomization procedure, for instance by checking whether background and substantive variables are equally distributed within and across groups.
If the study did not need or use a randomization procedure, one should check the success of the non-random sampling, for instance by checking whether all subgroups of the population of interest are represented in sample.
Other possible data distortions that should be checked are:

dropout (this should be identified during the initial data analysis phase)

Item nonresponse (whether this is random or not should be assessed during the initial data analysis phase)

Treatment quality (using manipulation checks).

Characteristics of data sample

In any report or article, the structure of the sample must be accurately described. It is especially important to exactly determine the structure of the sample (and specifically the size of the subgroups) when subgroup analyses will be performed during the main analysis phase.
The characteristics of the data sample can be assessed by looking at:

Basic statistics of important variables

Scatter plots

Correlations and associations

Cross-tabulations

Final stage of the initial data analysis

During the final stage, the findings of the initial data analysis are documented, and necessary, preferable, and possible corrective actions are taken.
Also, the original plan for the main data analyses can and should be specified in more detail or rewritten.
In order to do this, several decisions about the main data analyses can and should be made:

In the case of non-normals: should one transform variables; make variables categorical (ordinal/dichotomous); adapt the analysis method?

In the case of missing data: should one neglect or impute the missing data; which imputation technique should be used?

In the case of outliers: should one use robust analysis techniques?

In case items do not fit the scale: should one adapt the measurement instrument by omitting items, or rather ensure comparability with other (uses of the) measurement instrument(s)?

In the case of (too) small subgroups: should one drop the hypothesis about inter-group differences, or use small sample techniques, like exact tests or bootstrapping?

In case the randomization procedure seems to be defective: can and should one calculate propensity scores and include them as covariates in the main analyses?

Analysis

Several analyses can be used during the initial data analysis phase:

Univariate statistics (single variable)

Bivariate associations (correlations)

Graphical techniques (scatter plots)

It is important to take the measurement levels of the variables into account for the analyses, as special statistical techniques are available for each level:

Nominal and ordinal variables

Frequency counts (numbers and percentages)

Associations

circumambulations (crosstabulations)

hierarchical loglinear analysis (restricted to a maximum of 8 variables)

loglinear analysis (to identify relevant/important variables and possible confounders)

Exact tests or bootstrapping (in case subgroups are small)

Computation of new variables

Continuous variables

Distribution

Statistics (M, SD, variance, skewness, kurtosis)

Stem-and-leaf displays

Box plots

Nonlinear analysis

Nonlinear analysis will be necessary when the data is recorded from a nonlinear system. Nonlinear systems can exhibit complex dynamic effects including bifurcations,chaos, harmonics and subharmonics that cannot be analyzed using simple linear methods. Nonlinear data analysis is closely related to nonlinear system identification.

Main data analysis

In the main analysis phase analyses aimed at answering the research question are performed as well as any other relevant analysis needed to write the first draft of the research report.

Exploratory and confirmatory approaches

In the main analysis phase either an exploratory or confirmatory approach can be adopted. Usually the approach is decided before data is collected. In an exploratory analysis no clear hypothesis is stated before analysing the data, and the data is searched for models that describe the data well. In a confirmatory analysis clear hypotheses about the data are tested.

Exploratory data analysis should be interpreted carefully. When testing multiple models at once there is a high chance on finding at least one of them to be significant, but this can be due to a type 1 error. It is important to always adjust the significance level when testing multiple models with, for example, a Bonferroni correction. Also, one should not follow up an exploratory analysis with a confirmatory analysis in the same dataset. An exploratory analysis is used to find ideas for a theory, but not to test that theory as well. When a model is found exploratory in a dataset, then following up that analysis with a confirmatory analysis in the same dataset could simply mean that the results of the confirmatory analysis are due to the same type 1 error that resulted in the exploratory model in the first place. The confirmatory analysis therefore will not be more informative than the original exploratory analysis.

Stability of results

It is important to obtain some indication about how generalizable the results are.[34] While this is hard to check, one can look at the stability of the results. Are the results reliable and reproducible? There are two main ways of doing this:

Cross-validation: By splitting the data in multiple parts we can check if an analysis (like a fitted model) based on one part of the data generalizes to another part of the data as well.

Sensitivity analysis: A procedure to study the behavior of a system or model when global parameters are (systematically) varied. One way to do this is with bootstrapping.

Statistical methods

Many statistical methods have been used for statistical analyses. A very brief list of four of the more popular methods is:

General linear model: A widely used model on which various methods are based (e.g. t test, ANOVA, ANCOVA, MANOVA). Usable for assessing the effect of several predictors on one or more continuous dependent variables.

Generalized linear model: An extension of the general linear model for discrete dependent variables.

Structural equation modelling: Usable for assessing latent structures from measured manifest variables.

Item response theory: Models for (mostly) assessing one latent variable from several binary measured variables (e.g. an exam).

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