Statistical Techniques Introduction

Statistics is defined as a methodology of gathering data, analyzing it, understanding the data and forming appropriate conclusions from the analysis. Not many subjects are as broad or have as many important applications as statistics (Wooldridge & Jeffrey, 2013). Mathematicians, scientists and researchers in general rely on statistics to interpret the information they collect or encounter in their specific fields of work. In general, nearly everything that covers the collection, interpretation, manipulation and presentation of data is considered statistics (Armitage, Berry, 2011). This paper discusses various statistical instruments, their assumptions and their uses. In the end, a conclusion is given.

Pearson’s Correlation Coefficient

Pearson’s correlation coefficient, r, is a statistical instrument that looks at the strength and the direction of the relationship between any two variables. It is more accurately known as the Person product-moment correlation coefficient (Taylor, Jeremy 2010). Simply put, it is a statistical instrument meant to weigh the relationship between two related variables. For example, it can be used to understand the link between the time one spends revising for a test and his or her eventual performance. It could also be utilized to look at whether there is a link between duration of unemployment and depression.

One can also think of the coefficient as the line of best fit between the collected for two variables.

Assumptions

Assumption 1:

When using the coefficient, the assumption that the data is normally distributed is made. This is because one cannot evaluate the important or statistical significance of the correlation between two variables without bivariate normality. However, this assumption is not easy to evaluate so a more appropriate and practical method is often used. The method entails evaluating the normality of the variables individually. This can be done by utilizing SPSS Statistics to conduct the Shapiro-Wilk test of normality.

Assumption 2:

For Pearson’s correlation coefficient to be accurate the data from the two variables has to be measured at ratio/ interval level. In essence, they have to be continuous (Taylor, Jeremy 2010). Some examples of this kind of data include weight measured in pounds or kilograms, test scores measure between 0 and 100, intelligence measured utilizing the IQ score, study time measured in minutes or hours and so on.

Range

Pearson’s coefficient for ranges from -1 to +1

Examples of uses

It is thought that Pearson’s coefficient can be applied to many different types of investigations and analyses. For instance, Chinese scientists have used it to investigate the genetic divergence between different types of rice in the country (Armitage, Berry 2011)

The objective of this particular objective was to determine the evolutionary...

When the correlation was measured, it revealed a positive correlation of between 0.78 and 089. They rightfully concluded that the evolutionary potential was very high.
ANOVA

Overview

ANOVA is a statistical instrument that measures whether the results of a test, experiment or survey are significant. Whether they are important. Simply put, the ANOVA test is meant to help you decide whether or not to accept your null hypothesis (Armitage, Berry, 2011). Essentially, it tests different groups of data two see whether they are similar or different. There are several instances when the ANOVA test may come in handy (Wooldridge & Jeffrey, 2013). For example, when different types of therapies such as biofeedback, medication and counseling are tried for a group of psychiatric patients, the test can be used to see which therapy is more effective. Another example where the ANOVA test can be utilized is when a manufacturer used two different processes to make the same type of product (Taylor, Jeremy 2010). The test can be utilized in this case to find out which of the two products works better. Also, if university students from different campuses took the same test, examiners can use the ANOVA test to determine which campus outdid the rest.

Assumptions

· The groups being tested should have the same sample sizes

· The data is normally distributed or near normal distribution

· Population variances should be the same

· Samples should be independent

Range/uses

As mentioned before, the ANOVA test looks at whether the results of a particular study or test are significant. When doing the test, scientists often aim to answer two questions: (1) whether the variance/ difference between the groups is significant? (2) If yes, then how much variance is there between the groups?

Many tests often compare group SDs (Standard deviations), group medians, and group means (Armitage, Berry 2011). For group means, several types of measures are available including the Tukey HSD procedure. This procedure can reveal group differences by looking at plotting the means and pinpointing the cases where there is no overlap.

Example of uses

The ANOVA test is utilized to measure whether there is a significant difference between factors in response to some sort of stimuli (Wooldridge & Jeffrey, 2013). This has dozens of important applications. For example, the when a manufacturer uses two distinct procedures to make a bulb, he or she can use the test to determine which bulb is better. Another example, is when students from different countries do the same exam, ANOVA can be utilized to tell which group actually outperformed the other.

T-tests

Overview

The T-test is also a measure of difference/ variance between two groups. The t score is the ratio of the difference within a group and between the group…