Estimation and hypothesis testing, Biology tutorial

Introduction:

Researchers are fascinated in answering numerous types of questions.  For instance, a scientist might wish for to know whether the earth is warming up.  A physician may wish for to recognize whether a new medication will lower the blood pressure of a person.  An educator may wish to observe whether a new teaching method is better than a traditional one. These kinds of questions can be addressed via statistical hypothesis testing, that is a decision making procedure for assessing claims on a population.

Estimation:

Estimation is the total procedure of using an estimator to generate an estimate of a parameter. Estimation and hypothesis testing are interconnected. An estimate is any precise value of a statistic whereas an estimator is any statistic employed to estimate a parameter. For instance, the sample mean x is employed to approximate the populations mean µ. A Point estimate is acquired if a single number is employed to approximate a population parameter. For illustration s = 30.  An Interval estimate is acquired if a range of values is employed to approximate a population parameter. For instance, a range of values between 20 and 30 lets assessment of the estimate dissimilar the point estimate of the single value.

Statistical Hypothesis:

A statistical hypothesis is an assumption regarding a population parameter. This hypothesis might or might not be true. There are two kinds of statistical hypotheses for each condition, that is, the null hypothesis and the alternative hypothesis.

Null and Alternative Hypothesis:

There are two kinds of statistical hypothesis.

Null hypothesis: The null hypothesis, symbolized by H0, is generally the hypothesis that sample observations outcome purely from chance.

Alternative hypothesis: The alternative hypothesis, symbolized by H1 or Ha, is the hypothesis that sample observations are affected by some non-random cause.

For illustration, assume that we wanted to find out whether a coin was fair and balanced. A null hypothesis might be that half the flips would outcome in Heads and half, in Tails. The other hypothesis might be that the number of Heads and Tails would be much different. Symbolically, such hypotheses would be stated as:

H0: p = 0.5

Ha: p <> 0.5

Assume that we flipped the coin 50 times, resultant in 40 Heads and 10 Tails. Given this outcome, we would be inclined to refuse the null hypothesis. That is, we would wind up that the coin was perhaps not fair and balanced.

The level of Confidence:

In survey sampling, various samples can be arbitrarily chosen from the similar population; and each sample can frequently produce a dissimilar confidence interval. A few confidence intervals comprise the true population parameter; others don't.

A confidence level signifies to the percentage of all possible samples which can be estimated to comprise the true population parameter. For illustration, assume that all possible samples were chosen from the similar population, and a confidence interval was calculated for each sample. A 95% confidence level involves that 95% of the confidence intervals would comprise the true population parameter.

The word 'Level Of Confidence' (LOC) is employed to explain the percentage of instances which a set of similarly constructed tests will capture the true mean (that is, accuracy) of the system being tested in a particular range of values  around the measured accuracy value of each test.

Confidence intervals are made up of at a confidence level, such as 95%, chosen by the user. What does this signify? It signifies that if the similar population is sampled on many occasions and interval estimates are made on each and every occasion, the resultant intervals would bracket the true population parameter in around 95 % of the cases. A confidence stated at a (1 - α) level can be thought of as the inverse of the significance level (α).

Steps in Hypothesis Testing:

1) Each and every hypothesis testing situation starts with the statement of hypothesis.

2) Find out the kind of data, which is whether the data is discrete or continuous.

3) State the hypothesis. Be certain to state both the null and alternative hypotheses.

4) Design the study. This step comprises:

  • Choosing the correct statistical test.
  • Selecting a level of significance.
  • Preparing a plan to carry out the study.

5) Perform the study and gather the data.

6) Evaluate the data. Make the decision to refuse or not reject the null hypothesis.

7) Sum up the results.

When you refuse the Null Hypothesis, the five possibilities are:

1) There is direct cause and outcome among the variables. For instance, raise in height of an Okro plant fetches about raise in its yield. 

2) There is a reverse cause and outcome relationship among the variables.

3) The relationship among the variables might be caused by a third variable.

4) There might be a difficulty of interrelationships between numerous variables.

5) The correlation might be coincidental.

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