in this video we'll take a look at null
and alternative hypotheses
now the null hypothesis means there's no
effect or nothing happened or there's no
difference the null hypothesis is often
represented by H Sub Zero and it makes a
statement about the population not the
sample so in other words we put
population values or symbols in our null
hypothesis now the alternative
hypothesis is really the opposite it
states or it means that there was an
effect or something happened or there
was a difference the alternative
hypothesis is often represented by H sub
1 or H sub a
and it also makes a statement about the
population not the sample so if we take
a look at these two side-by-side once
again in review the nulls stated by H
Sub Zero the alternative is H sub 1 or H
sub a the null basically states nothing
happened and look at the opposite here
the alternative States something
happened or the null can state no effect
the alternative states there was an
effect and finally the null can state no
difference effectively and the Altera
would state the opposite there was a
difference and once again both
hypotheses refer to the population let's
go ahead and take a look at an example
using the Pearson correlation or
Pearson's R correlation measures the
degree of the linear relationship if
there's any at all between two variables
it's known as Pearson's R let's go and
take a look at the null and alternative
hypotheses for correlation or for
Pearson's R here in words the null would
state there is not a relationship
between the two variables in the
population the alternative would state
the opposite it would state there is a
relationship between the two variables
in the population
notice how the null States no effect or
there's no relationship whereas the
alternative states there is an effect or
there is a relationship using symbols we
could say the following the null and
that little thing that looks like a P
there that stands for a row and it's the
correlation in the population so we
would say null Rho XY equals 0 and then
the alternative would say Rho XY does
not equal 0 or in other words the null
would state there's no correlation
between x and y two variables in the
population whereas the alternate would
state there is a correlation between the
two variables x and y in the population
and zero here means no relationship in
correlation so when the null says it's
equal
zero and saying there's no relationship
when the alternative says it's not equal
to zero its stating there is a
relationship
so in review the null states there's no
effect or zero relationship whereas the
alternative states there is an effect or
a non zero relationship now hypotheses
need to be mutually exclusive and
exhaustive exclusive means there's no
overlap between the null and the
alternative and if you look at our two
statements up above where it says that
row XY equals zero row XY does not equal
zero notice that those do not overlap at
all equals and not equals are completely
non overlapping it's either zero which
is the null in that case or it's not
zero which is the alternative so they're
completely exclusive they do not overlap
and then exhaustive means they must
cover or exhaust all possibilities the
null and alternative when taken together
and notice that they do as every
possible value for Pearson's R is either
zero or not zero so it does exhaust all
possibilities so once again it's
exclusive because they don't overlap and
it's exhaustive because they cover all
possibilities
now notice how the alternative has a not
equal sign implying that the alternative
hypothesis can be either greater than 0
or less than 0 or in other words
correlation can be positive or negative
this is known as a two-tailed test since
the alternative hypothesis consists of
two possibilities either greater than 0
or less than 0 alternatively one tailed
test can also be used in hypothesis
testing and we'll examine one tailed
tests in another video ok that's it
thanks for watching