Session 2a Flashcards
what is a Hypothesis
Assumption/prediction made about a population parameter (NOT about a sample estimate)
Ad campaign A is preferred to B
Getting $1 million will make people happier 6 months later
Drug A will increase survival rate of AIDS patients
these are example of what
hypotheses
Traditionally, experimental research engages in a procedure for what
hypothesis testing (NHST)
what is (NHST)
Null hypothesis signifiance testing
is NHST used still
NHST is still widely used
More recent approaches focus on effect sizes and formation of confidence intervals
what are the Steps for Hypothesis Testing
Step 1: Set Up a hypothesis
Step 2: Choose α (significance level)1
Step 3: Examine your data and compute the appropriate test statistic
Step 4: Make the decision whether to “reject” or “not reject” the null hypothesis
Alternatively, look at the signifiance level (p-value) for the test statistic value
explain Step 1: Set Up a hypothesis
Usually a prediction that there is an effect of certain variable(s) in the
population Example:
Eating fries will give you high cholesterol
Null and Alternative Hypothesis
what is null hypothesis
(H0)
This is what we test statistically
No effect (“People will have equal cholesterol regardless of how many fries they eat”)
what is Alternative Hypothesis
(H1)
Research/experimental hypothesis
Some effect (“People eating more fries will have higher cholesterol than those who eat less fries”)
Sometimes Ha is used to denote the alternative hypothesis
what is Step 2: Choose α (alpha) (significance level)1
Decide the area consisting of extreme scores which are unlikely to occur if the null hypothesis is true
Proportion of times we are willing to accidentally reject H0, even if H0 is true
Conventionally, α = what
.05 or α = .01
The cutoff sample score for α is called what
the critical value
explain Step 4: Make the decision whether to “reject” or “not reject” the null hypothesis
Compare the calculated value of your test statistic to the critical value for α
in step 4, If your value is greater than or equal to the critical value what happens
reject H0. Otherwise, retain H0
a decision to reject H0 implies what
acceptance of H1
explain Alternatively, look at the signifiance level (p-value) for the test statistic value:
Such values often given by SPSS, R, or other statistical software If p ≤ α (e.g., p ≤ .05), what do you do to the null
reject H0. Otherwise, retain H0
this is a yes/no decision
If H0 is rejected, you may conclude what
that there is a statistically significant effect in the population
“Eating fries has a statistically significant effect on cholesterol levels”
“statistically significant” effect does not indicate what
We have a precise estimate of the effect
The effect is important or meaningful
explain how ‘stat sig’ does not indicate that We have a precise estimate of the effect
It may be that an effect is “significant”, but there is some error around our estimate
The amount of error is represented in the standard error for the estimate The effect may be smaller or larger than our estimate
explain how ‘stat sig’ does not indicate The effect is important or meaningful
Suppose we find that eating 1kg fries/month leads to 10g weight gain Is 10g really a meaningful amount?
Weight gain may be “significant” if it was observed from many people
what is a Confidence Interval
gives us information about the precision of our estimates
Example: a 95% confidence interval (CI) may indicate that true weight gain in the population is between 2g and 18g per month
We don’t know for sure that a 95% CI will contain the true value of the effect in the population
If we repeated our experiment many times, 95% of the time a 95% CI will contain the true effect
for Confidence intervals, Usually, we form {(1 − α) × 100}% CIs meaning what
If α = .05, we form a 95% CI
If α = .01, we form a 99% CI
for Confidence intervals, As sample size increases what happens to your estimate
our estimate becomes more precise
And our CI intervals may become smaller or more narrow
As α decreases what happens to the CI
Our CI intervals become larger or wider
how to Calculate an effect size
A standardized measure of the magnitude of a treatment effect Commonly used measures of effect size:
Pearson’s correlation coefficient (r) or correlation ratio squared (R2) Cohen’s d
Omega (ω) or omega squared (ω2)
Eta squared (η2)
Effect sizes are useful for what
assessing the importance of our effects
how to determine if an effect is small or large
r = .10 (small effect) r = .30 (medium effect) r = .50 (large effect)
what are the Two types of errors in hypothesis testing
Type I: Reject H0 when it is true (False Positive)
Type II: Retain H0 when it is false (False Negative)
Hypothesis Testing About a Single Mean - z-test
what is the purpose
Based on the sample mean (X) we test whether the population mean
(μ) is equal to some hypothesized value
Hypothesis Testing About a Single Mean - z-test, Prior Requirements/Assumptions:
The variable, X, in the population is normally distributed
The population standard deviation, σ, must be known
The sample must be a simple random sample of the population (independence of observations)
Computing a z-test for a single mean is like calculating what
a Z-score for your sample mean
look at snapshots to understand z (standard) scored
on desktop
A distribution of standard scores have Mean = what
0
A distribution of standard scores have Standard Dev of what
Standard Deviation (SD) = 1
If μ and σ are used, we get a z-score for the individual relative to who
other people in the population
If the distribution of scores follows a normal distribution, a Z-score transformation will transform all scores to what
a standard normal distribution
aka The shape of the distribution does NOT change, only the units
explain X ∼ N(μ,σ^2) → Z ∼ N(0,1)
for z-score
“~” means “distributed as” or “follows. . . ” (some distribution)
“N” is notation for “Normal” with “(Mean,Variance)” in parentheses
If scores are on standard normal distribution what can we do
more easily interpret them
what is μ0
the value of μ under H0, sometimes called a test value
what is σX -
is the standard deviation for the sampling distribution of X
σX - is the standard deviation for the sampling distribution of X
Special name for this concept is what
standard error
What is a sampling distribution?
Suppose we conduct our experiment a million times
Each time, we obtain a sample of N = 25 McGill Psyc 305 students and a different value for mean IQ: X
σX is the SD for the resulting sampling distribution:
If α = .05 (two-tailed), then our critical value, zcrit,α/2, is about what
1.96
If α = .05 (two-tailed), then our critical value, zcrit,α/2, is about 1.96
If H0 is true…
About α/2 = 2.5% of observed z-tests will be less than -1.96 About α/2 = 2.5% of observed z-tests will be greater than 1.96 2.5% + 2.5% = 5% (desired level for α)2
Limitations of z-test
Knowing the true value of the population standard deviation (σ) is unrealistic
Except in cases in which the entire population is known
what is the alternative to the z-tes
t-test
