Statistics Hypothesis testing – lesscss

By | November 23, 2018

Statistics – Hypothesis testing

A statistical hypothesis is an assumption about a population
which may or may not be true. Hypothesis testing is a set of
formal procedures used by statisticians to either accept or
reject statistical hypotheses. Statistical hypotheses are of two
types:

  • Null hypothesis, ${H_0}$ – represents a hypothesis of
    chance basis.

  • Alternative hypothesis, ${H_a}$ – represents a
    hypothesis of observations which are influenced by some
    non-random cause.

Example

suppose we wanted to check whether a coin was fair and balanced.
A null hypothesis might say, that half flips will be of head and
half will of tails whereas alternative hypothesis might say that
flips of head and tail may be very different.

$ H_0: P = 0.5 \[7pt] H_a: P ne 0.5 $

For example if we flipped the coin 50 times, in which 40 Heads
and 10 Tails results. Using result, we need to reject the null
hypothesis and would conclude, based on the evidence, that the
coin was probably not fair and balanced.

Hypothesis Tests

Following formal process is used by statistican to determine
whether to reject a null hypothesis, based on sample data. This
process is called hypothesis testing and is consists of following
four steps:

  1. State the hypotheses – This step involves stating both
    null and alternative hypotheses. The hypotheses should be
    stated in such a way that they are mutually exclusive. If one
    is true then other must be false.

  2. Formulate an analysis plan – The analysis plan is to
    describe how to use the sample data to evaluate the null
    hypothesis. The evaluation process focuses around a single
    test statistic.

  3. Analyze sample data – Find the value of the test
    statistic (using properties like mean score, proportion, t
    statistic, z-score, etc.) stated in the analysis plan.

  4. Interpret results – Apply the decisions stated in the
    analysis plan. If the value of the test statistic is very
    unlikely based on the null hypothesis, then reject the null
    hypothesis.

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