# Statistics

Brainstorming is a technique for creating ideas. The tool is the first technique that is applied in analysis. Ideally, analysts are expected to come up with creative ideas or to develop the ideas that are outside of the mainstream way of thinking. Osborn, who claimed that the technique was better than individual thinking, introduced the term in the 1950s. Unlike individual thinking, brainstorming allows or promotes sharing and development of ideas. This is a significant aspect, since it enhances the development of ideas. Osborn has developed the four basic rules for effective brainstorming. The rules are meant to allow group participation and create the quality of the resultant solution.

The first rule focuses on quality. This rule states that an effective brainstorming activity should have diversity in terms of ideas. Obviously, the higher the number of available ideas is, the better the chances of coming up with a solution are. Thus, group leaders should encourage members to contribute ideas. The second rule in effective brainstorming requires members/leaders to withhold criticism (Triola, 2001). In this case, the group members are discouraged from giving negative comments regarding the topic given. Thus, members are not supposed to comment negatively about a certain suggestion or person. The third rule involves acceptance or welcoming of ideas. This rule requires members to be optimistic about the possibility of existence of more than one solution, to a particular problem. Thus, the group members are expected to view all suggestions as possible solutions. Moreover, the rule also allows the group to consider those solutions that are outside of the solution sphere. The underlying assumption is that extreme ideas give better chances of identifying the limits, within which a solution lies. Finally, effective brainstorming allows combination of ideas. Indeed, most solutions have more than one dimension. This implies that the best solution can only be achieved through a combination of respective ideas.

**Scatter diagrams**

A scatter diagram is an effective tool for analysis of two variables. The tool allows a researcher to visualize the type of relationship that exists between to variables. Consequently, the tool gives a quick verification of existence of a relationship between the two variables. Mainly, scatter diagrams are used in order to verify cause-and-effect relationships (Jarrell, 1994). However, the tool cannot be used to prove or disapprove that one variable causes change in another variable. Thus, scatter diagrams can be used to investigate cause-effect type theories. The tool can also be used in the design of control systems.

Scatter diagrams showthe degree of correlation between the two variables. In particular, a scatter diagram will indicate either of the following correlations:

(a) Strong Positive Correlation;

(b) Weak Positive Correlation;

(c) No Correlation;

(d) Weak Negative Correlation;

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(e) Strong Negative Correlation.

A flow chart is a graphic tool used in order to represent a process or an algorithm. Normally, flow charts are made up of series of various types of boxes that are connected using arrows. Consequently, a flowchart can be used to represent steps used to derive a certain solution. When representing a process, each of the boxes within a flowchart gives a specific step through the process, while the arrows represent the actual process. Ideally, flowcharts are used to analyze, design, or manage processes.

Like other design tools, flowcharts enable us to visualize a process in a more effective manner. Moreover, the tool enables viewers to establish the areas of possible bottlenecks, flaws and other less noticeable features (Neyman & Pearson, 1933). In any flow chart the direction of connecting arrows is very critical. In most cases, the direction of the arrow cannot be interchanged, since it will indicate a reverse or a new process. Most flowcharts, in particular those, representing a process or an algorithm, often have a start and an end-point. The start point indicates the input, while the end-point represents the resultant product. Thus, a flow chart is specifically designed for a particular problem or solution. Different symbols are used to represent various steps on a flow chart. For example, the “start” is usually represented by a rounded rectangle. Other generic steps are represented using normal rectangles. However, the choice of symbols depends on the researcher and the role of a flow chart. The following figures give some examples of the flow charts.

**Fishbone diagrams**

The fishbone diagram is a design tool used to establish the different causes or the possible causes of a certain effect. The tool is mainly used during the brainstorming stage. Ideally, the tool enables people to sought and to categorize the ideas according to ttheir level of applicability. As the name suggests, fishbone diagrams resemble a fish skeleton. In practical application fishbone diagrams are constructed in a right-to-left manner. Small “bones” are included at the each stage in order to incorporate details, which can be either causes or solution strategies. Professor Kaoru Ishikawa designed the tool for quality management applications. The tool was initially developed as a quality control tool, though it acquired other uses as well. Effective application of this tool involves four basic steps. The first step involves problem identification. This step requires the analyst to indentify the characteristics of the supposed problem. The second step requires the analyst to identify other consequential problems or factors that are associated with the main problem (Nancy, 2004). These possibilities or consequential problems are included into the first stage. The third stage involves identification of possible causes. Causes are incorporated into the diagram as shorter lines originating from the main “bone.” The final stage involves a detailed analysis of the identified problems/causes. Through this stage an analyst identifies or connects various problems with the respective cause. Moreover, the stage also allows the analyst to indentify the causes of a problem according to their order of agency. The complexity of a fishbone diagram depends on the number of identified problem/causes. The following is an example of the fishbone diagrams.

**Hypothesis Tests **

Hypothesis testingrefers to the process of differentiating alternative hypothesis using probability distribution data. The technique is a core course in statistic, and it is a fundamental aspect of statistical language. In statistic, a hypothesis is a tentative answer to a certain problem. Thus, hypothesis tests are used to determine the hypothesis that best fits a certain statistical problem. There are two types of hypotheses; namely, null and alternative hypotheses. The null hypothesis is normally denoted as H_{0}; it is the type of hypothesis that usually denotes chance (Moore, 2003). On the other hand, alternative hypothesis only involves non-random causes. In hypothesis testing an analyst is required to account for different types of errors. For example, type I error occurs, when a rejected null hypothesis is found to be true. This type of error is more significant to the researcher, than type II error. In most cases, analysts try to minimize the probability of committing type I error. Consequently, type II error occurs, when an accepted null hypothesis is found to be untrue.