He used statistics as a drunken man uses lampposts; for support rather than illumination by Andrew Lang, best known as collector of folk and fairy tales

hypothesis testing
Source: luminousmen.com

Understand Hypothesis testing and it's various terms in a simple way

Well, Hypothesis testing is concerned with making decisions using data. In statistics, it is a way for you to test results of survey or experiment to see if you have meaningful results.

 Hypothesis can really be anything if you can put it to the test🙋

 But before testing you need to understand how to write hypothesis statements, right?. It may be the most confusing topic in the statistics, to encounter with that you need to understand it through the statements. If you are going to make/build a hypothesis, it is customary to write a statement.
The two important part in the statement is "if" and "then". Yes, that's right every statement has to go with these two terms. Like :

 "IF I do this.......(independent variable) THEN it will happen to......(dependent variable)"
  •  If I study more then will get more marks
  •  If I stop spending money on unnecessary things then it will save more money
  •  If I practice football daily then my skills will improve for sure
  •  If I do exercise on daily basis then my fitness will improve
I think now you can understand how it works through these few example but note, you have to include "if" and "then", include both independent and dependent variable, testable by an experiment.

Classical hypothesis testing is concerned with deciding between two decisions. The first, a null hypothesis is specified that represents the status quo. Usually labeled as H0. This is what we assume by default. The alternate or research hypothesis is what we require evidence to conclude. Labeled as H𝞪 or sometimes H1. So to reiterate, the null hypothesis is assumed true and statistical evidence is required to reject it in favor of a research  or alternate hypothesis.

Steps to perform testing  

  1. Figure out your null hypothesis
  2. Build your alternate hypothesis
  3. Choose what kind of test you need to perform
  4. Determine a significance level and compute p value
  5. Draw conclusions. Either support or reject null hypothesis

hypothesis
Source: google instructionalwikigroup

Case Study: Public Opinion About President

Source: Brooks/Cole, a division of thomson learning, Inc.
On May 16, 1994, Newsweek reported the results of a public opinion poll that asked: “From everything you know about Bill Clinton, does he have the honesty and integrity you expect in a president?” (p. 23). Poll surveyed 518 adults and 233, or 0.45 of them (clearly less than half), answered yes. Could Clinton’s adversaries conclude from this that only a minority (less than half) of the population of Americans thought Clinton had the honesty and integrity to be president? 
Null hypothesis: There is no clear winning opinion on this issue; the proportions who would answer yes or no are each 0.50.
Alternate hypothesis: Fewer than 0.50 or 50%  of the population would answer yes to this question. The majority do not think Clinton has the honesty and integrity to be president.
Summarizing data into a test statistic: Sample proportion is 233/518 = 0.45
Standard deviation = 0.022
Test statistic: z = -2.27
P-value: proportion of bell shaped curve below -2.27 = 0.0116
Making a decision:  The p-value is less than 0.05, so we conclude that the proportion of American adults in 1994 who believed Bill Clinton had the honesty and integrity they expected in a president was significantly less than a majority.

P-Value

This value is the most common measure of statistical significance. Their ubiquity, along with concern over their interpretation and use makes them controversial among statisticians.
A Statistical hypothesis test may return a value called p-value. It is the quantity that we can use to interpret the result of a test and either reject or fail to reject the null hypothesis. This is done by comparing the p-value to a threshold value chosen beforehand called the significance level.
A common alpha value used is 0.05 or 5%.

  •  If p-value > alpha : Fail to reject null hypothesis
  •  If p-value<alpha : Reject null hypothesis
Some non-parametric or distribution-free statistical hypothesis tests do not return p-value instead, they might return a list of critical values and their associated significance levels as  well as a test statistic.

  • If test statistic < critical value : Fail to reject null hypothesis
  • If test statistic > critical value : Reject the null hypothesis


Errors in Tests

Sometimes the evidence of the test may suggest an outcome and be mistaken.
  • Type I Error: Incorrect rejection of a true null hypothesis/false-positive.
  • Type II Error: Incorrect failure of rejection of a false null hypothesis/ false-negative.

Some common names of Hypothesis tests

  • Pearson's Correlation Coefficient
  • Spearman's Rank Correlation
  • Chi-Squared Test
  • Fried man test
  • Kruskal-Wallis H test
  • ANOVA
  • F test
  • Z test
  • Wald test
  • MANCOVA
  • KPSS test

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