math

Kinds of Statistical Tests

The Parametric Tests

To use the parametric tests, some conditions should be met. The data must be (1) normally distributed, and (2) the level of measurement must be either interval or ratio. The data

are considered normal when the value of skewness equals zero, and the value of kurtosis is 256.

The interval data provide numbers that reflect a difference among items. With interval scales, the measurement units are equal. Examples are scores of intelligence tests and time as reckoned from the calendar. They have no true zero value.

The ratio scale is the highest type of scale. The basic difference between interval and ratio scales is that the interval scale has no true zero value. Common ratio scales are measures of length, width, weight, capacity, and loudness and many other things (Parametric Statistics, 2017).

The non-parametric tests.

The nonparametric tests do not require normality of the distribution. Since skewness is the measure that will tell whether the data is normal or abnormal. If the value of skewness is either positive or negative, the distribution is said to be abnormal. Aside from skewness, there is kurtosis that also tells whether the data is normal or abnormal. If the value of kurtosis is greater than or less than 0.265, then the distribution is said to be abnormal. Under these test, the levels of measurement are the nominal and ordinal data. Nominal data include male and female, yes or no responses, political affiliations like LP, LDP, Lakas, religious groupings, Christian and non-Christian and other organizations. Ordinal data include Strongly Agree, Agree, No Opinion, Disagree and Strongly Disagree, and other data that employ rankings.

The t-Test for Independent Samples

The t-tests are used to determine the significance of the difference between the two means. It is useful when samples are less than 30, and the standard deviation is unknown. The

following assumptions have to be met: Data are normally distributed, and measurement levels are expressed in interval and ratio scales.

1. The t-test for independent samples is used when the samples are drawn from a different population.

2. The t-test for correlated samples is used when the samples come from the same population or the same set of samples is subjected to two different experimental conditions.

A two-tailed test is used when we predict a relationship but do not predict the direction in which scores will change. A one-tailed test is used when we predict the direction in which scores will change. To compute the t-statistic, you must first calculate the sample variance (or standard deviation) as a substitute for the unknown value.

Steps in Solving for the t-test.

1. State the null hypothesis and the alternative hypothesis.

2. Select the appropriate test statistic and its distribution under HO.

3. Choose a level of significance () and determine the critical or rejection region of the test. 4. Formulate the decision rule for rejecting or failing to reject the null hypothesis.

5. Compute the value of the t-test.

6. State the conclusion based on the decision made.

The t-test for Correlated Groups

It is a test that checks whether there is any significant difference between the population means of two groups. It is used when two correlated groups of data (interval or ratio) are being compared.