This is for taking surveys.
The Null hypothesis for the above
experiment is that the observed values
are close to the predicted values. The
alternative hypothesis is that they
are not close to the predicted values.
These hypotheses hold for all Chi-
square goodness of fit tests. Thus in
this case the null and alternative
hypotheses corresponds to:Null
hypothesis: The coin is fair
Alternative hypothesis: The coin is biased

The chi-square test for independence
is used to determine the relationship
between two variables of a sample. In
this context independence means that
the two factors are not related.
Typically in social science research,
we're interested in finding factors
which are related, e.g. education and
income, occupation and prestige, age
and voting behaviour.
Example: We want to know whether boys
or girls get into trouble more often
in school. Below is the table
documenting the frequency of boys and
girls who got into trouble in school
H1 = There is no relationship
Variables are Independent.
H2 = There is a relationship
Variables are dependent.
If Chi-Square is greater than
the 5% value in the table
=> H2 => 95% chance that there
is signaficant relationship.
Variables are dependent.
Degrees of Freedom = (Row - 1)*(Column -1)
This is a 2 by 2 Table for the Chi-Square Calculation!
Do you like Coke or Pepsi?

========> Coke*****Pepsi*****Totals
=> Male => === ====
***Female => === ====
**Totals ==> === ====

Chi-Square=> Degrees-of-Freedom =>
This is a 2 by 3 Table for the Chi-Square Calculation!
Do you like Coke or Pepsi or Orange-Crush?

========> Male*****Female*****Totals
**Coke => ****** ******
**Pepsi => ****** ******
Orange => ****** *****
**Totals ==> === ====

Chi-Square => Degrees-of-Freedom =>
This is a 3 by 3 Table for the Chi-Square Calculation.


Chi-Square => Degrees-of-Freedom =>
This is a 4 by 1 Table for the Chi-Square Goodness of Fit Calculation.
If you know what the percents are and type them in => Click gg4()
If each percent is calculated and equal Click gg5()

Observed ***
*Percents ***
Expected ***

Chi-Square => Degrees-of-Freedom =>

Hypothesis testing refers to the process of using statistical analysis to determine if the observed differences between two or more samples are due to random chance (as stated in the null hypothesis) or to true differences in the samples (as stated in the alternate hypothesis). A null hypothesis (H0) is a stated assumption that there is no difference in parameters (mean, variance, DPMO) for two or more populations. The alternate hypothesis (Ha) is a statement that the observed difference or relationship between two populations is real and not the result of chance or an error in sampling. Hypothesis testing is the process of using a variety of statistical tools to analyze data and, ultimately, to fail to reject or reject the null hypothesis. From a practical point of view, finding statistical evidence that the null hypothesis is false allows you to reject the null hypothesis and accept the alternate hypothesis.