Week 7 day 1 Flashcards
What is the mean and standard deviation of Z scores?
0 and 1 respectively.
What is the equation for t-test for one sample, if we know the population mean and standard deviation?
z=(X-mean)/sd, where X is the observed score.
What are the four steps Andy talks about when it comes to constructing a statistical test?
- We need a test statisitic, T.
- We need a sampling distribution of T, if the Null was true
- We need the observed T from our data.
- We need a rule that maps every value of T onto a decision about whether or not we reject the Null or not. Usually in the form of alpha < .05.
In a t-test, what are we comparing?
The mean of our sample to the known mean of a population, or the mean of another sample.
What does it mean the bigger t is?
The bigger the t-statistic is, the more different the sample mean is to either the population mean or the mean of another sample.
Why do we use the standard error of the mean when we do not know the standard deviation of the populatio when calculating a t-statistic?
When we do not know the standard deviation of a population, but do know the mean, the t-statistic is calculated in the following way:
t=(sample mean-population mean)/sample sd/sqrt(N)
sample sd/sqrt(N) is the standard error of the mean. This is a better estimate of the population standard deviation than the sample sd by itself, as it takes into account sample size. I don’t quite get why it is a better estimate….
What is one of the assumptions required for doing t-test?
That the underlying distribution is normal.
What influence does a larger sample size have on the distribution of the t-statistic ?
The distribution of t-statistics is normal (this has been proved mathematically and we do not need to do this). The bigger the sample size the tighter the normal distribution of the t-stat.
What is Cohen’s d?
It is the effect size used for t-tests.
It is calculated as follows: d = (data mean - populatioon mean)/sd dev.
Very similar to z-score, but use whole data set and not just a single data point.
What does a Cohen’s d of 1.5 mean?
The mean of the sample data is 1.5 standard deviations higher than the population mean.
When reporting results and stats for a test, what is the key information that need to be included?
- Descriptive stats, e.g. mean and sd if doing a t-test.
- The null hypothesis.
- The stat test done and its results and whether these results are statistically significant.
- The interpretation of those results, i.e. what this test shows.
If a t-stat is negative and p-value is significant, then what does this mean?
The mean of the sample is significantly LOWER than the population mean (if doing a one sample t-test with a known population mean).
