Statistical Tests and Procedures

The method of making decisions based on scientific study is called statistical test. What has been predicted as unlikely to have happened by chance alone is considered as statistically significant in statistics.

Statistical tests known as test of significance determines what outcomes lead to the rejection of null hypothesis for a level of significance. The result is called statistically significant if it has been predicted as unlikely to have occurred by sampling error alone, according to the significance level.

Hypothesis tests are used in determining what outcomes of a study would lead to a rejection of the null hypothesis for a pre specified level of significance.An alternative framework is to specify a set of statistical models, and use model selection techniques to choose the most appropriate model.

Statistical Tests and Procedures: Example of Philosopher's beans

Generations before the hypothesis testing was formalized and popularized the given example was provided by a philosopher :

Few beans of this handful are white.
Most beans in this bag are white.
Therefore: Probably, these beans were taken from another bag.
This is an hypothetical [sic] inference

Example of the Philosopher's beans : Statistical Tests and Procedures

Population in the example: Beans in the bag.
Sample: Handful beans.
Null hypothesis: Sample originated from the population.

The null-hypothesis is rejected based on the obvious difference in appearance. The consideration of a real population and a real sample produced an imaginary bag as the result. This example which the philosopher was considering is based on logic than the probability. This example requires the probability calculation and a comparison of that probability to a standard in order for this to be a real statistical hypothesis test

Statistical Tests and Procedures

• Analysis of variance (ANOVA): ANOVA models are used to analyze the differences between group means and the variation among and between the groups.
• Chi-squared test: This is a hypothesis in where when the null hypothesis is true when the sampling distribution of the test statistic is a chi-squared distribution.
• Correlation: Correlation means the dependence between the statistical relationship between two random variables or two sets of data.
• Factor analysis : This describe the variability among observed and correlated variables with reference to factors which are unobserved variables.
• Mann–Whitney U : This a hypothesis that a particular population tends to have larger values than the other.
• Mean square weighted deviation (MSWD) : Measures of goodness of fit.
• Pearson product-moment correlation coefficient : This is a measure of the degree of linear dependence between two variables.
• Regression analysis : Estimating the relationships among variables.
• Spearman's rank correlation coefficient : Measure of statistical dependence between two variables.
• Student's t-test : This is used to determine if two sets of data are significantly different from each other.
• Time series analysis : This is a sequence of data points, measured at successive points in time.