PSYC 210- Hypothesis Testing
In hypothesis testing, a Type I Error is: A. rejecting the null hypothesis when the null hypothesis is false B. rejecting the null hypothesis when the null hypothesis is true C. failing to reject the null hypothesis when the null hypothesis is true D. failing to reject the null hypothesis when the null hypotheses is false
B. rejecting the null hypothesis when the null hypothesis is true
The average 8th grader is 61 inches tall. My 8th grade class is 66 inches tall, and I think we are exceptionally tall! What would the null hypothesis be in this case?
***My class is taller than the average 8th grade class The differences between my class and the average height are due to chance u (the mean) is greater than or equal to 61 u is equal to 61
I want to see if more than 30% of registered voters in my county voted in the primary election. Which of these is an appropriate alternative hypothesis?
***greater than or equal to (>=) 30% of voters came out to vote less than (<) 30% came out to vote exactly 30% of voters came out to vote (= 30%) Some number other than 30% of registered voters voted (not = 30%)
What does setting an alpha of 0.01 mean? Choose all that apply.
1. There is 1% or less of a chance of falsely rejecting the null hypothesis 2. My Type I error rate is 1% Explanation: Alpha is our Type I error rate, which is the same as setting the false positive rate (or rate of rejecting the null hypothesis when there are actually no differences in the data).
What are the 6 steps in hypothesis testing?
1. define the null and alt. hypothesis 2. setting type 1 error 3. identify statistical test 4. determine critical region 5. collect data 6. make decision
A researcher says that her analysis shows that the result of her one-sample t-test is statistically significant. This means that the mean of her sample is: A. very likely to be predictable B. very unlikely to occur by chance C. very likely to be found again upon replication D. very unlikely to be large
B. very unlikely to occur by chance
The alternative hypothesis for an independent samples, two-tailed t-test states __________. A. µ1 < 0 B. µ1 not equal to µ2 C. µ1 + µ2 = 0 D. µ1 > µ2
B. µ1 not equal to µ2 Feedback:We want to test whether the two groups are equal to one another, therefore our alternative hypothesis is that they are not equal
What type of test is most appropriate when you want to compare an outcome between two groups with different people in each group? A. Z-test B. Paired t-test C. Independent samples t-test D. t-test for correlations
C. Independent samples t-test
H0 (null hypothesis) vs. H1 (alternative hypothesis)
H0 Equal (=) H1 Not equal (≠) H0 Greater than or equal (≥) H1 Less than (<) H0 Less than or equal (≤) H1 Greater than (>)
For which of these should we use an independent samples t-test?
I want to see whether college students have more friends than professors do, on average I want to see whether people drink more when they are more distracted I want to see whether over 30% of people who sign up for an event on facebook actually show up for that event I want to see if people are happier before or after my stats class Explanation: Independent t-tests allow us to compare two group's means to each other. The only example that includes two groups is the first choice, college students vs. professors.
Which of these is the appropriate null and alternative hypothesis test for the following question: are senior citizens less anxious than the average adult? Let's say the average anxiety level is a 45 on a scale of 80.
Null: mu >= 45, Alternative: mu < 45 Explanation: Since we are interested in seeing whether older adults have LOWER anxiety, our alternative hypothesis would be that they DO have lower anxiety, or mu < 45. Then, the null is that it is not lower, or that mu >= 45.
degrees of freedom
Number of quantities minus constraints on those quantities Ex. i know the sample mean. So if i know the values of all but 1 of my participants. I can figure out that person's score given the mean. So this is a value that can't vary 4 values vary 5th value varies around the mean Number of independent pieces of information (contributors of variance) that went into calculating our statistic Df is always n-1
assumptions about independent-samples t-test
Normality Independent events Both samples have equal-ish variance (homoscedasticity)
p-value
The probability of observing a test statistic as extreme as, or more extreme than, the statistic obtained from a sample, under the assumption that the null hypothesis is true. -the probability of being more extreme than our observed z-score
The ____ the confidence intervals, the ____ sure we are of where the true mean is.
larger; less smaller, more
A paired t-test is the same as
running a one-sample t-test on the sums of the values Explanation: Paired t-tests are just like one-sample t-tests looking at the comparison, or the differences, between the values of each measurement.
critical z score
the z-value cut-off(s) at which our significance level (alpha) is met
observed z-score
the z-value we calculate for out data
When we assume sampling distribution is normally distributed, events are independent, and know SD of the population, should we use t-test or z-test?
z-test
A sampling distribution can help us answer hypotheses about our sample's relation to the population mean because
***we can calculate the probability of getting our sample's value or higher to see if it's likely to be part of the same population both are normal distributions so we can convert between them we can compare the standard deviation of our sampling distribution to the standard deviation of our population we can compare our sample's value and the population's value visually on a sampling distribution Explanation: We are curious whether the values in our sample are so extreme that they might be in a different population instead of those in our population, or if they are fairly similar and perhaps differences are due to chance. We can do this by calculating probabilities using z-scoring, etc.
types of t-tests
-independent -repeated measures -one sample
t-test can compare...
1. Mean of sample against population mean 2. Mean of 2 separate sample to each other 3. means of 2 measures to each other within a single sample
pooled variance
A single measure of sample variance that is obtained by averaging two sample variances. It is a weighted mean of the two variances.
What type of test is most appropriate when you want to compare an outcome between the same people at two different time points? A. Paired t-test B. Independent samples t-test C. t-test for correlations D. Correlations and regressions
A. Paired t-test
In hypothesis testing, a Type II Error is: A. failing to reject the null hypothesis when the null hypothesis is false B. rejecting the null hypothesis when the null hypothesis is false C. failing to reject the null hypothesis when the null hypothesis is true D. rejecting the null hypothesis when the null hypothesis is true
A. failing to reject the null hypothesis when the null hypothesis is false
The p-value of our result is a measure of: A. the probability of finding a sample with a mean as or more extreme than ours B. the critical value that we compare our test statistic against C. the probability of getting a sample with our mean D. our Type I error rate
A. the probability of finding a sample with a mean as or more extreme than ours
For the given scenario, choose the appropriate alternative hypothesis for my situation. My research question is: Do people who play video games regularly have better hand eye-coordination than the rest of the population? Say that we can measure hand-eye coordination as reaction time in a sports task and the population has a mean reaction time of 600 ms. A. µ > or = 600 B. µ is not equal to 600 C. µ < 600 D. µ > 600
C. µ < 600 D. µ > 600
t-test
Compares mean values of a continuous variable between 2 categories/groups.
Which of these is NOT an assumption we make before we run an independent samples t-test? A. Independence B. Homogeneity of variance (homoscedasticity) C. Outcomes are normally distributed D. The two samples are the same size
D. The two samples are the same size Feedback:We don't need sample size to be the same when using independent samples since we account for the sample size of each in the equation for the t-score. We do care about this in paired samples t-tests, though!
If we were testing whether a particular sample was drawn from a population with a particular mean and the standard deviation of the entire population was known, we would use the _____-test to statistically answer the question. A. r B. t C. F D. Z
D. Z
What if confidence intervals included negative values?
It could be the mean difference is zero and we should retain the null because both means might match
When we have a significant but a small effect size, this means
Our effect is real but maybe not practically important Explanation Effect size gives us a sense of how big the difference really is (when we have a significant effect). This is essentially a measure of its importance!
one sample t test
compares the mean of a random sample from a normal population with the population mean proposed in a null hypothesis
paired/ repeated measure t-test
Repeated measures (within subject): difference b/n 2 sample means; 2 measurements within one sample Ex. word test vs math test
In my research, I find that senior citizens' anxiety levels fall around a z-score of -1.54 compared to the mean. If our critical z-score is -1.65 for an alpha = 0.5, what should we do?
Retain the null hypothesis Explanation: Since our z-value is not more extreme than the critical cut off, we retain our null hypothesis and say that seniors' anxiety is not different than the average adult
Type I error (alpha)
Stating that there is an effect when none exists (accepting an expirimental hypothesis when the null is true)
significance level (alpha)
The acceptable level of error selected by the researcher, usually set at 0.05, 0.01, or 0.001. The level of error refers to the probability of rejecting the null hypothesis when it is actually true for the population. -Probability of a Type I error, i.e. probability of rejecting a true null hypothesis; the largest risk of rejecting a true null hypothesis that a researcher is willing to take
alternative hypothesis
The hypothesis that states there is a difference between two or more sets of data Ex. my class is better than the average (>65)
power analysis
This is the probability that we do reject a null hypothesis when it is truly false Increase power by: reduce error variance -better measures, more homogenous population Increase sample size- decreases standard error the mean
how to calculate the means of paired sample t-test
We calc the different b/n our means mean post- mean pre Null: post minus pre less than or equal to 0 Alter post minus pre greater than 0
Cohen's d
a measure of effect size that assesses the difference between two means in terms of standard deviation, not standard error
Type 2 error (beta)
accepting the null hypothesis when it is false and the alternative hypothesis is right
The degrees of freedom of an independent t-test is calculated by
adding together the groups' sample sizes and subtracting 2 Explanation: The degrees of freedom of the two samples is the same as the added degrees of freedom of each sample, so N1-1 + N2-1 which gives us N1+N2-2
Independent t-test
between subject, unpaired; difference b/n two sample means; 2 different groups of ppl ex. placebo vs drug treatment group
We use t-tests when we
don't have the population standard deviation
confidence interval
estimations of where the population mean might be; range for the true mean
effect size
how big is the difference b/ n the true population parameters and the ones assumed by the null hypothesis; measure of the importance of our findings -If we find a significant result but the effect size is mall it means that the difference may not be all the interesting
z test
hypothesis-testing procedure in which there is a single sample and the population variance is known
What is the appropriate alternative hypothesis for this research hypothesis: College students differ from professors in how many friends they have.
mean friends of college students < mean of professors mean friends of college students is not equal to mean of professors mean friends of professors - mean of college students > 0 mean friends of college students + mean of professors is not equal to 0 Explanation This is an independent samples t-test that is two-tailed, so we want a not equal to sign. The only one that fits here is option B.
Pick the correct t-test to use in this scenario: I think that people's strength changes from the morning to the afternoon. I will measure how much each person can deadlift as soon as they wake up and then around 3pm in the afternoon.
paired t-test Explanation Since each individual is doing both tests, we are comparing two measurements within the same sample. This would call for a paired t-test!
When we don't know standard deviation, should we use t-test or z-test?
t-test
hypothesis testing
testing out expectations through experience is my sample mean far enough away from my population mean? Ex. is my stats class so different from the average score of a stats class that i should say that my class is special
null hypothesis
the hypothesis that there is no significant difference between specified populations, any observed difference being due to sampling or experimental error -differences due to chance Ex. my class is no better than the average of 65 (<65)
confidence intervals tell us
the range that the alternative mean might be in with some confidence level Explanation The confidence interval gives us a 95% probability of the true alternative mean being in a specific range