Hypothesis

"Estimation" is the aspect which a corporate manager deals most frequently.  All managers must make quick estimates too.  The outcome of these estimates often have financial repercussions.  There are two types of estimates, viz. (1) Point estimate and (2) Interval estimate.

 

If an estimate of a population parameter is given by a single value, then the estimate is called point estimate of the parameter.  But if an estimate of a population parameter is given by two distinct numbers between which the parameter may be considered to lie, then the estimate is called an interval estimate of the parameter.  As the value of a point estimate fluctuates from sample to sample, interval estimates are often preferred to point estimates.  Also the interval estimate indicates the accuracy of an estimate. 

 

The Building blocks of hypotheses are variables.  A variable is anything that varies, changes, or has differences.  Something that never changes is called a constant.  Variables that only have two extremes are called attributes.  In research, one deals with mostly two variables, independent and dependent.  Independent variables are those thought to be the cause or bring about change in other variables.  Dependent variables are those things changed or affected by independent variables, sometimes through other variables. 

 

Hypotheses are simply if-then statements that can be categorized in certain logical forms, such as no difference (null hypotheses), associated difference, directionality of difference and magnitude of difference.  A good hypotheses implies all these.  A hypothesis is an assumption or supposition made as a basis for further reasoning in terms of a quantitative statement about the population under exploration.  The more specific the hypotheses, the better.  Not only do statistics in research become more powerful with specific hypotheses, but one can engage in confirmatory research instead of exploratory research.  An important part of the research process that goes along with hypotheses formulation in constructing your operational definitions. 

 

For research to be effective and sound, the use of the scientific method is a pre-requisite.  Hypotheses is essential to skeptically demonstrate the relation between the variables (both dependent and independent) and validate the research.  It enables us to do away with vague approaches and meaningless interpretations.  It establishes the relationship of concept with theory and specifies the test to be applied especially in the context of a meaningful value judgement.  It plays a pivotal role in the scientific research method.  Hypothesis is formed on the basis of observation and is very much a part of the scientific method to validate a research project. 

 

PROCEDURE FOR TESTING HYPOTHESES

 

1.         Set up hypothesis

 

This involves stating the hypothesis about the population parameter after taking sample statistic and finding the difference between hypothesized parameter and sample statistic.  There are two types resorted to, viz. Null Hypothesis and Alternative Hypothesis.  The statement of Null Hypothesis suggests that there is no significant difference between the population and the sample.  The statement of Alternate Hypothesis is that there is a material difference between the population and the sample.  The steps in formulating a hypothesis are elaborated below:

 

a)     It begins with stating the hypotheses – by making an assumption about the population parameter.

b)     We determine the significance level and specify a value for it, say "x".

c)     Then we gather sample data and determine the sample statistic.

d)     Determine the probability that the sample statistic would diverge as widely as it has from expectations, specify a value "y".

e)     If the difference between (x) and (y) is large then we automatically reject the null hypothesis. If the difference is small, we accept it.

f)       If the difference between (x) and (y) is material, we automatically accept the alternative hypothesis.  If it is immaterial, we reject it.

 

2.         Set up the Significance Level

 

The level of significance is very important since it determines the basis on which a hypothesis is accepted or rejected.  A significance level of 10% means that the level of confidence is 90%. 

 

3.         Set up a Test Criteria

 

The next step is to select an appropriate Probability Distribution for the particular test.

 

 

4.         Perform Computation

 

Thereafter, computations are made on the data obtained from the random sample regarding its mean and standard error.

 

5.         Make the Decision

 

The last step is to take decisions like accepting or rejecting the null hypothesis which in turn leads to a decision on the problem actually being addressed.

 

ERRORS IN HYPOTHESES

 

Whilst selecting a sample population -

 

v      Non-sampling errors are caused by deficiencies in the collection and editing of data.  Three reasons for such errors include procedural bias, biased observations and non-response bias.  Procedural bias is the distortion of the representativeness of the data due to the procedure adopted in collecting the data.  Absence of response can lead to non-response bias.  Biased observations are observations that do not correctly reflect the characteristics of the population being studied.

 

v      Sampling errors are the differences between the value of the actual population parameter and the sample statistic.  Samples are used to arrive at conclusions regarding the population.  For example, the sample mean is computed to arrive at an estimate of the population mean.  However, the sample mean may not be equal to the population mean.  The difference between the two means would be the sampling error.

 

Whilst testing the hypothesis –

 

v      Type I Error is committed when the null hypothesis is true, but the test rejects it.

v      Type II Error is committed when the null hypothesis is false, but the test accepts it.