inferential statistics

inferential statistics:

Mathematical approach to deducing the probability of the occurrence of a characteristic in a population based on the measured characteristics of a sample

-        we reject the null in the sample when null is false in the population

-        we retain the null in the sample when null is true in the population

Significance in statistics

means probably true

o    Infers that relationship is not simply due to randomness or chance but that there is truly a relationship between the variables

-        Significance in power

o    Power: increase chances of rejecting a false null hypothesis

o    Test the null hypothesis, either reject if false or retain if true

What is probability

Likelihood of something occurring

o    Even if we find a statistical difference in our groups, there is the possibility that our decision may not be correct

Type 1 error:

we reject the null hypothesis in our sample, even though the null hypothesis is true for the population               

o    Researcher must base his or her conclusion on the evidence of a relationship between independent and dependent variable.

o    In actuality, the difference may not be because of independent variable, but may be due to

o    Chance

o    The way we conducted the expirement

Type 2 error:

we retain the null hypothesis in our sample, even though the null hypothesis is false for the population

o    Retain the null hypothesis in our sample, even though the null hypothesis is false in the population

o    By reducing risk of type I error, we increase chance of type II error

o    We don’t like type two error because we don’t want to miss something that works

o    How do we decrease type 2 errors

§  Increasing treatment effectd

§  Decreasing measurement errors

§  Using a more sensitive design

§  Best way is to increase sample size

what do we mean by p<.05 or p<.01

less than 5% chance of type 1 error

o    Significance level given is how willing we are to make a type I error

o    p < .05 we are making a type one error less than 5 times out of 100

o    Can range from 0 to 1, commonly see .05, .01, and .001

o    Smaller P, less likely to make a type I error (saying something works when it doesn’t)

What is done to control error

-        Reduce type I error by reducing significance level

-        Tradeoff is increasing risk of type II error and losing power

General Linear Model: basis for most statistical analyses in social research

-        A system of equations that is used as the mathematical framework for most the statistical analyses used in applied social research

T -tests:

good statistical procedure to see if means of two groups are significantly different

-        Significant relationship between a nominally scaled independent variable with two levels and a dependent variable that is interval or ratio in scale.

-        Are means of groups different enough

T test and power: - we can increase the power of a t-test in three ways

o     1. Show a greater difference in the means of the two groups by using a better and stronger treatment

o    2. Reduce variance in groups by applying treatments more consistently and using control variables to reduce difference between participants

o    3. Increase number of subjects in study

When T is found to be significant, we are saying that the true variance exceeds the error variance