Exam 2 (Ch. 5-8) Statistics for the Behavioral Sciences (Bauer,
Fall 2021)
One hypothesis: experimental results
merely come from sampling the origi-
nal population at random (not a different
population)
null hypothesis the hypothesis that there is no signifi-
cant difference between specified pop-
ulations, any observed difference being
due to sampling or experimental error.
H0: ¼1-¼2o=r0¼1=¼2
gives us the probabilities of means, as-
suming the null hypothesis is true
We know IQ is normally distributed, with
¼ = 100a nd à = 15.
Sampling distribution of the mean The sampling distribution is also a nor-
mal distribution, with standard error
equal to ¼ = 100a nd à = 15.
We can use the standard normal table to
answer questions about probabilities
What patterns or trends your results
show you
alpha (±)level: The amount of risk you
decide to take in your decision.
When the chance of being wrong is low
enough (i.e., the p level is lower than the
alpha level you set) we say that we reject
the null hypothesis. When this happens,
Interpretation of results
we state that the results are statistically
significant.
If the p level is greater than alpha, we
"accept" the null hypothesis. Generally
researchers prefer to say that they fail to
reject the null hypothesis - they have in-
sufficient evidence for rejecting it. These
results are not statistically significant.
If my p level is less than alpha, we reject
Factors for significance the null hypothesis and say that my re-
sults are statistically significant
, Exam 2 (Ch. 5-8) Statistics for the Behavioral Sciences (Bauer,
Fall 2021)
tells us whether a result is likely due to
chance or to some factor of interest
probability of my result or bigger if the null
hypothesis is true
P level’ area beyond z
p levels
As the calculated z gets larger, the cor-
responding p level gets smaller
rejection region
An interval allows us to express how
much confidence we have in the accura-
cy of the interval
General procedure: start with a point esti-
confidence intervals
mate in the center, then add and subtract
a certain amount from there
The narrower the interval, the more pre-
cise your estimate
Estimation
Confidence intervals are good for 3 Precision or error
things We are going to be able to use it to test
a null hypothesis (hypothesis testing)
1) Put point estimate of mean in the cen-
ter
2) Mark off the same distance above and
below the point estimate (mean) æ How
much distance?
3) Depends on level of confidence
Constructing a Confidence Interval (CI) Depends on level of confidence æ CI =
how confident you are that a theoretical
interval contains the true µ (or other pa-
rameter) ** æ± = .05 (100-.05) = 95%CI; ± =
.01 (100-.01) = 99% Cl
We created a 99% confidence interval, 100% we use it to create the mean, it is
what is the probability that this interval always in the interval
contains the sample mean? Contains population mean: 99%
Fall 2021)
One hypothesis: experimental results
merely come from sampling the origi-
nal population at random (not a different
population)
null hypothesis the hypothesis that there is no signifi-
cant difference between specified pop-
ulations, any observed difference being
due to sampling or experimental error.
H0: ¼1-¼2o=r0¼1=¼2
gives us the probabilities of means, as-
suming the null hypothesis is true
We know IQ is normally distributed, with
¼ = 100a nd à = 15.
Sampling distribution of the mean The sampling distribution is also a nor-
mal distribution, with standard error
equal to ¼ = 100a nd à = 15.
We can use the standard normal table to
answer questions about probabilities
What patterns or trends your results
show you
alpha (±)level: The amount of risk you
decide to take in your decision.
When the chance of being wrong is low
enough (i.e., the p level is lower than the
alpha level you set) we say that we reject
the null hypothesis. When this happens,
Interpretation of results
we state that the results are statistically
significant.
If the p level is greater than alpha, we
"accept" the null hypothesis. Generally
researchers prefer to say that they fail to
reject the null hypothesis - they have in-
sufficient evidence for rejecting it. These
results are not statistically significant.
If my p level is less than alpha, we reject
Factors for significance the null hypothesis and say that my re-
sults are statistically significant
, Exam 2 (Ch. 5-8) Statistics for the Behavioral Sciences (Bauer,
Fall 2021)
tells us whether a result is likely due to
chance or to some factor of interest
probability of my result or bigger if the null
hypothesis is true
P level’ area beyond z
p levels
As the calculated z gets larger, the cor-
responding p level gets smaller
rejection region
An interval allows us to express how
much confidence we have in the accura-
cy of the interval
General procedure: start with a point esti-
confidence intervals
mate in the center, then add and subtract
a certain amount from there
The narrower the interval, the more pre-
cise your estimate
Estimation
Confidence intervals are good for 3 Precision or error
things We are going to be able to use it to test
a null hypothesis (hypothesis testing)
1) Put point estimate of mean in the cen-
ter
2) Mark off the same distance above and
below the point estimate (mean) æ How
much distance?
3) Depends on level of confidence
Constructing a Confidence Interval (CI) Depends on level of confidence æ CI =
how confident you are that a theoretical
interval contains the true µ (or other pa-
rameter) ** æ± = .05 (100-.05) = 95%CI; ± =
.01 (100-.01) = 99% Cl
We created a 99% confidence interval, 100% we use it to create the mean, it is
what is the probability that this interval always in the interval
contains the sample mean? Contains population mean: 99%
