CHAPTER TEN

HYPOTHESES TESTING

10.1Introduction

You will learn what a hypothesis is and the many kinds of hypotheses in this chapter. There are certain fundamental ideas in testing hypotheses that you will learn, like level of significance, degree of freedom, type I and type ii error, etc. You should consequently be able to do statistical analysis in your research investigations after reading this chapter.

10.2Objectives

At the end of this chapter, you should be able to:

  1. define hypothesis and its types.

  2. describe some basic concepts in testing hypothesis

  3. enumerate the procedure for testing hypothesis and explain each step involved.

10.3Hypothesis

Hypothesis is a term referred to be an assertion subject to verification or an assumption used as a basis of action. Hypotheses are, therefore, assertions or an assumption made and not established facts. It is a sign of how seriously researchers take the solutions to their stated research challenges. When a hypothesis is tested, the findings can produce new information or validate already-known knowledge. A theory is supported by a hypothesis if it can be tested, validated, and verified to be true. In other words, the process of evaluating hypotheses in research involves testing and confirming theories, which advances knowledge.

10.3.1Types of Hypotheses

Hypotheses are stated into forms: null hypothesis and alternative hypothesis. A null hypothesis denoted by (H0) is a hypothesis that is stated in the form no difference or no relationship between variables under analysis.

An alternative hypothesis (Ha) stated in the form, a difference or relationship exists between two populations or between two parameters of two populations. It is hypothesis that is retain when the null hypothesis is rejected. The alternative hypothesis sometimes refers to be directional if it shows the direction of difference or relationship, while non-directional does not show the direction of difference or relationship between variables under analysis.

10.4Significance Level Selection

Selection of the level of significance is sometimes known as alpha level (α) or significance level. In psychological and educational research, the alpha level is expressed at.05 and.01 levels of significance. When we set our alpha (significance) level at.01, we are indicating that if the research is repeated 100 times, 99 out of 100 times, the same result will occur, and 1 out of 100 times, the result may differ owing to risk. However, if it is set at.05, it indicates that if the research is repeated 100 times, you can be certain that 95 of the results would be accurate, while 5 of the 100 results might differ owing to chance variables or risk factors.

Anytime, a Researcher is stating a null hypothesis, it is very important to give it a chance of rejection. On this basis, the data collected by the Researcher for analysis is at a point of rejection, you must specify the level at which to bear the risk. This risk is stated in probability level for being true or false. It can also be considered as the amount of error involved in a given statistical decision about the null hypothesis. This therefore indicates that selection of a specific level of significance, precisely the amount of error risk involved in the decision.

10.5Degrees of Freedom

The term degree of freedom means the number of independent observations or values in a sample that are free to vary when computing a test statistically. It is the probability that the test will lead to a decision to reject H0 when H0 is indeed false. Take for instance, you have a sample 30 cases, the degree of freedom is 30—1 = 29. This means that 29 of the 30 observations are chance to vary and hence (n—1) degree of freedom. In another way, you ask your Students in class that add three to 5 to get 25. In this instance, 5 is a fixed number, while other numbers are flexible. N is the total number of observations or chances, and 1 is the fixed variable, hence the degree of freedom is N—1. As you will see later, different statistical tests use different methods to determine the degree of freedom.

10.6Type I and II Errors

When the calculations are made correctly, the Researcher will make correct decision about null hypothesis, but still can commit two possible errors in decision making about null hypothesis. However, a Type I mistake occurs when a correct null hypothesis is rejected when it should have been preserved. The symbol for this is alpha (α).

In the opposite direction, if you accept the null hypothesis rather than reject it when it is wrong, you are incorrect. Type II mistake is the acceptance of a false null hypothesis when it ought to have been rejected. Beta serves to indicate the mistake (\\beta ).

Note that the Researcher is trying to minimize type I error and type II error by stating the level of significance at 0.1 to 0.5. if the probability of accepting a false (H0) is '\\beta ' then the probability of rejecting a false H0 is 1—\\beta . this is known as the power of the statistical test.

10.7One-tailed and Two-tailed Tests

Because the null hypothesis does not reveal the direction of the difference, the test is always two-tailed. For instance, a null hypothesis claims that there is no connection between academic success and motivational level.

One-tailed test is used when the hypothesis is presented and shows the direction of the association. For instance, academic success and motivational level are significantly correlated.

10.8Testing of Hypothesis

Testing of hypothesis is kind of decision-making process in a research work. It is an idea to verify the proposed null hypothesis of its benefit of doubt. This opportunity for rejecting null hypothesis can also be viewed as the strategy for choosing between hypotheses and it involve severed steps. These steps are as followed:

Step 1: Stated statement of hypothesis.

Step 2: Selecting the significance (alpha) level (α)

Step 3: Choosing relevant test statistic and applied it to obtain values from sample data

Step 4: Determining the critical region (i.e., rejection and acceptance region)

Step 5: Making valid decision based on the result (i.e., statistical decision)

Step 6: Conclusion.

10.8.1Statement of Hypothesis

Hypothesis is stated to guide the research activities, and the Researcher, therefore there is the need to verify the statement through the process of hypothesis testing.

10.8.2Selecting of Alpha Level

A researcher’s study effort must include testing the hypothesis. The alpha level and degree of freedom allow the researcher to make an informed judgment on whether to keep or discard the hypothesis. Additionally, it helps to reduce type I and type II errors in research studies.

10.8.3Statistical Decision

A Researcher, after computing all values for the test statistically, it is now left to compare calculated value with critical values in the table, that enable to accept or reject the hypothesis. Since you are aware of level of significance and concept of degree of freedom in our previous units.

10.8.4Drawing Conclusion

After statistical decision, the next action is to draw conclusion. The conclusion is drawn based on the results obtained.

10.9Choices of Appropriate Statistical Tools

Whenever a researcher wants to describe the general nature and characteristics of a given sample, the researcher uses descriptive statistical, such as percentage, frequency distribution table, and cumulative frequency and graphical representation of data (bar, frequency polygon, histogram, pie chart etc). Furthermore, the appropriate descriptive measure that uses a score to describe or represent others in the sample is measure of central tendency (i.e. mean, mode and median). While the appropriate descriptive measure for relative position is sigma score, percentile, quartiles, rank and standard scores (Z or T- scores). In descriptive statistics the generalization is limited to the particular group of the research, i.e, the generalization of the descriptive statistical measures is limited to the sample of the research. This implies, no conclusion could be extended beyond the sample of the study. In addition, it also provides valuable and useful information about the nature of the sample only. In the other hand, inferential statistics can be use if the data obtained is either parametric or non-parametric and the followings statistical tools that can be used for testing hypothesis are:

  1. Correlations or Relationships: The researcher that wants to find out correlations or relationships between variables. If the basic assumptions for parametric is meant. The researcher makes use of Pearson Product Moment Correlation (P. P.M.C) statistics. But a situation if conditions of basic assumptions of parametric are not meant, the researcher makes use of Spearman Rank correlation (Rho) or chi-square (x2)

  2. Differences: The researcher that wishes to investigate the differences between variables the appropriate statistics tools are discuss below:

  3. The researcher makes use of t-test if it is parametric data and has single sample with population mean.

  4. The researcher makes use of t-test statistic if the data collected is parametric nature with two samples.

  5. The researcher makes use of Analysis of Variance (ANOVA), if the data obtained is parametric with three or more samples.

  6. The researcher makes use of krustall-wallis test if it is non-parametric.

  7. Effects/Influence: The appropriate statistical tools for finding out interactive effects /influence are:

  8. The researcher employs the use of Analysis of Co-Variance (that is per-test Vs post-test), Two-way ANOVA (i.e. interactive between two variables), if it is parametric (interactive effects).

  9. The researchers equally use Two-way ANOVA (i.e. interaction between two variables), if it is parametric (influence).

Choice of Appropriate Statistical Tool on the Basis of Measurement Scales

  1. Nominal scale: It is measurement which does not bear any magnitude relationship to one another, the appropriate statistical tools for hypotheses testing under this data are Signed test, Chi-square, Phi-coefficient etc.

  2. Ordinal scale: This measurement at this level which bears only magnitude and possess all the attributes of nominal scales, the appropriate statistical tools used for analysing are Spearmen rank correlation, Rank sum, U-test, Krustal-wallis.

  3. Interval scale: This scale has all the attributes of nominal, ordinal and equal interval between measurements of units. The researcher makes use of T-test, ANOVA, Correlation analysis etc.

  4. Ratio scale: This scale has properly of absolute zero and has all attributes of nominal and interval. To test hypotheses for this scale measurement the researcher makes use of Z-scale, Measures of Central Tendency, ANOVA, ANCOVA.

Student Activity

  1. Distinguish between the following pairs of concepts.

  2. Level of significance and degree of freedom

  3. Type I error and Type II error

  4. One-tailed and two-tailed test.

  5. Explain the following terms

  6. P < 0.01

  7. Alternative hypothesis

  8. Null hypothesis

  9. Power of statistical test.

  10. Briefly describe the procedure for testing of hypothesis in a research study.

References

Awotunde, P.O & Ugodulunwa, C. A. (2002). Introduction to Statistical Methods in Education. Printed and Published in Nigeria by Fab. Anieh (Nig) Ltd.

National Teachers’ Institute, Kaduna & National Open University of Nigeria (2016) Basic Research Methods in Education.