The manipulation of
statistical formulas is no substitute

for knowing what one is doing.

Hubert M Blalock Jr

Chapter 10

Sec 10.2

The second type of statistical
inference about a population based on information from a sample is "TEST of
SIGNIFICANCE". These tests have a goal of assessing evidence provided by
the data about "some claim" about the population.

Claim: "I make 80% of my free throw attempts in basketball."

"Cola drinks lose
sweetness over time."

"Student over the
age of 30 have better attitudes toward school."

Validating these statements (or refuting them) is done through a significance test.

Significance tests answer two
questions:

a) does the sample results (however small) reflect the true parameter

b) would the outcome result easily be explained by chance

Procedures:

1) careful statement of alternatives

2) identification of the parameter of interest

3) clear statement of the alternatives: "null hypothesis" and
"alternative hypothesis"

The NULL HYPOTHESIS (H _{0 }pronounced "H-nought") declares that there is NO effect or
change in the population. |

The ALTERNATE HYPOTHESIS (H _{a}) declares that there is some effect or change in the
population. |

A significance test works by asking..."How unlikely is the observed outcome if the null hypothesis were really true" by assigning a number called the P-value which designates the probability that the Null Hypothesis is true).

Remember "p" for probability. The p values are calculated
from Table A or by using normal cdf as before.

Generally, we begin by assuming that the null hypothesis is TRUE and attempt to
disprove it by finding a very low likelihood that it is true, thereby making it
false. We then accept the alternate hypothesis as true.

LOGIC: IF the probability of a result is very low then the result is SURPRISING, with a capital "S" and provides strong evidence against the original assumption (hypothesis). |

Recap:

**Small p values are evidence against the Null Hypothesis
because they say that observed result is unlikely

to occur just by chance. Large P-values fail to give evidence against the
Null Hypothesis.

How small must a P-value be to persuade us to reject the null
hypothesis???

Rule of Thumb: P-value less than .05 is called STATISTICALLY SIGNIFICANT.

Let's see how all this works.

Next