kok Flashcards
What is hypothesis testing
Based on the normal curve which is a probability distribution based on the theory
probability distribution between groups
What is the simplest form of hypothesis testing
it involves determining if two groups are significantly different
Ex. Compare 2 groups (teenagers vs. middle-aged people)
What happens when both sample means are equal, or there is no difference between the 2 groups?
null hypothesis or Ho
If there is no real difference between groups, we expect X1 - X2 = 0
What happens when the sample means are NOT equal, or there is a difference between 2 groups?
alternative hypothesis or Ha
The sample means of the different groups have a significant difference
Can we observe quantitative mean difference from our sample even if in reality the groups do not significantly differ?
Yes, means may differ due to chance. This is what sampling error is
Explain the degree or risk of error we are willing to make in hypothesis testing
We cannot ensure that we will not commit the error of concluding that Ho is false when in reality it is true
this risk is called aplha
What is alpha
The probability of error
What are the four basic steps of hypothesis testing?
State the Hypothesis
Set the level of significance
Compute the test statistic
Make a decision
Explain why we state the hypothesis
In all efforts to test a hypothesis, there are two types of hypothesis
Ho = there is no difference between 2 groups
Ha = there is a difference between 2 groups
Explain Ho or Null hypothesis
No difference between means
two samples drawn from the same N
Any observed difference is due to chance or sampling error alone
Explain Ha or alternative hypothesis
Difference between means
there is an effect
Two samples drawn from the same N
Observed difference due to the variance or manipulation
What do we want to reject
The null hypothesis
we want to accept alternative hypothesis
What is falsifiability criterion
In order to support Ha (our real hypothesis), we need to falsify the Ho
What is the sampling distribution of differences between means
assumed reality that Ho is true
frequency distribution of a large number of differences between sample means that have been randomly drawn from a given population
What happens if the assumed reality when Ho is true
Most sample mean differences fall close to zero
few sample mean differences fall far from zero
if the difference between groups is small then we accept Ho and conclude difference is due to chance or sampling error alone
what happens if the difference between groups or sample means is so large
we reject Ho and conclude there is a true difference
how to determine when a difference between means is large enough, to conclude that is statistically significant difference?
the answer or cutoff point is set by the level of significance or alpha level
By convention, a is set at .05 or .01
what does the expected sample mean difference fall mean
Data will fall within 95% confidence interval = Data likely if Ho is True
Sample mean difference falls oustide the 95% CI = Data unlikely (unexpected) if Ho is true ( if observed mean difference fall outside the 95% CI or area of rejection, we reject Ho)
What is the relationship between the size of alpha and the hypothesis
The larger the alpha, the larger the area of rejection; the easier it is to reject Ho and support the Ha (more likely to make error)
The smaller the alpha, the smaller the are of rejection; harder it is to reject Ho and support Ha (less likely to make an error)
What does the certain level of alpha state
The certain level of alpha is our willingness to risk error
T or F
We are always certain that we have made the correct decision
False
We can only be certain by given a level of confidence
risk of making an error is measured by alpha
What is type 1 error
We reject Ho in reality Ho is true (we concluded that there is a difference when in reality there’s none)
What is type 2 error
We fail to reject Ho when in reality Ho is false (we conclude that there is no difference when in reality there is)
What type is more dangerous
committing both types are dangerous depending on the situation
How to reduce type 1 error
Set a lower significance level leading to a more stringent decision of rejecting Ho
Make it more difficult to reject Ho by making alpha lower
How to reduce type 2 error
Increase the sample size or the significant level leading to a bigger chance of rejecting Ho
Make it easier to reject Ho by making the alpha larger
How do we compute for the test statistic
Using either spss or manually computing
What is another definition of alpha in terms of making a decision?
alpha is the probability of obtaining the minimum required or theorized sample mean difference for us to reject Ho
What is the p-value
the probability of obtaining the actual observed sample mean difference
we compare both p and a to make a decision
probability of obtaining the difference between means by chance
when to reject Ho
p mist be less than alpha (p<a) to reject Ho
if p<a, we reject Ho
if p is > or = a, we fail to reject Ho (accept Ha)
where is the P value in the graph to make a decision
If P is in critical region, we reject Ho (p < a)
If P falls within the acceptance region, we accept Ha and fail to reject Ho (p >/= a)
What is statistical power
the probability of correctly rejecting a false Ho or getting a significant result when there is a real difference in the population
power is the probability that the test will identify a treatment effect if it really exists
how does statistical power increase
when any of P, Sample size, Effect size increases
what is effect size (r)
measure of the strength of a relationship or effect
it will tell you the size of the difference between two groups
T or F
Can there be non-significant, notable, effect size especially in low powered tests
Yes, unlike significance, effect sizes are not influenced by sample size
effect size is a simple way of quantifying the size of the difference between 2 groups
what is the interpretation of effect size
.10-.30 = small effect
.30-0.50 = medium effect
.50 - above = large effect
what does a small or large ES mean
a small es can be impressive if variable is difficult to change (increase in life expectancy)
a large ES doesn’t necessarily mean that there is any practical value if it isn’t related to the aims
what is the difference between significance and effect size
Effect size quantifies the size of the difference, and can be the true measure of significance of the difference
significance is the likelihood that the difference could be an accident of sampling (p-value)
statistical significance is not the most important; it is the effect size
