1.state your research hypothesis in the form of a relation between two variables. 2. find a...
TRANSCRIPT
1. State your research hypothesis in the form of a relation between two variables.
2. Find a statistic to summarize your sample data and convert the above into statistical hypothesis:
Statistical hypothesis: > 0 1 - 2 < 0
3. Set a straw man, i.e., null hypothesisNull hypothesis: = 0 1 - 2 =
0.
4. Set the alpha level and conduct the statistical test with the assumption that the null is true.
5. Make a decision with potential errors.
Sampling Distribution of a Statistic
Imagined and theoretical
μ=72μ=72
nX
Population Sampling Distribution
μ=72μ=72 μ=72
nX
Sample size N = 36
μ=72
nX
Sample Size N = 16
μ=72
μ=72μ=72
nX
Sample Size N = 36
Central Limit TheoremCentral Limit Theorem
The mean of the sampling distribution of means (any statistic) equals the population mean (any parameter).
The standard deviation of the sampling distribution of means (any statistic) equals the population standard deviation divided by the square root of sample size. This is called the standard error of means.
The sampling distribution of means is normal independent of the pattern of the population distribution, given a large enough sample size (e.g., n = 30)
An example:
Hypothesis: Chinese children today are overweight.
Choose a statistic: Mean weight
Past records: = 50 lb; = 30 lb
H1: > 50 lb
H0: = 50 lb
<.01
n = 225 children ages 7 to 9; 55X
μ=50
2X
2.32 5.2Xz
55X
2225
30
nX
5.22
5055
XX
Xz
Reject Null
Point estimate:
55X1.64-1.64
28.58,72.51
264.155
64.1
XX CI90
55X
Interval estimates:
An example:
Hypothesis: Children’s weight differs from past.
Choose a statistic: Mean weight
Past records: = 50 lb; = 30 lb
H1: 50 lb
H0: = 50 lb
<.01; two tails, <.01/2 or <.005 at each tail
n = 225 children ages 7 to 9; 55X
μ=50
2X
-2.58 2.585.2Xz
55X
: Type II error
: Type I error Power
Actually True Actually False
NOT reject
Reject Decision
Null Hypothesis
μ= 50 z = 1.96
H0: μ = 50
H1: μ > 50
.05 Reject Null
β
power
μ= 50 z = 1.96
H0: μ = 50
H1: μ > 50
Reject Null
β
power
.01
power
β
μ= 50
H0: μ = 50
H1: μ > 50
.05
Reject Null
z = 1.96
Large NLarge N
Small NSmall N
power
β
.05
H0: μ = 50
H1: μ > 50
Reject Null
μ= 50 z = 1.96