z
The distributions of many variables approximate a normal curve, a mathematically defined, bell-shaped curve that is unimodal and symmetric.
As sample size increases does it become less or more normal
Normal
What has to be normal for the sample size to be normal
the population
what does a bell curve discribe
the distrubtution of many varibles
standardization
converts individual scores to standard scores for which we know the percentiles (if the data are normally distributed). Standardization does this by converting individual scores from different normal distributions to a shared normal distribution with a kn
whats do z scores help us do
z scores give us the ability to convert any variable to a standard distribution, allowing us to make comparisons among variables.
z score
A z score is the number of standard deviations a particular score is from the mean.
what do we need to calculate a z score
The only information we need to convert any raw score to a z score is the mean and standard deviation of the population of interest.
what mean does a z distribution always have
0 has mean and a standard deviation of 1
...
distribution is a normal distribution of standardized scores� a distribution of z scores. And the standard normal distribution is a normal distribution of z scores.
why are z scores useful
z scores give us a sense of where a score falls in relation to the mean of its population (in terms of the standard deviation of its population).
z scores allow us to compare scores from different distributions.
z scores correspond to known perctiles that
to find percentile what do you do with regards to adding and subtracting 50
above the mean= you add 50
below the mean = subtract 50
why is standardization helpful
helps us compare a meaningful compar of two distributions with different variables. we accomplish this be transforming raw scores from different distributions to z scores
Central limit therom
he central limit theorem refers to how a distribution of sample means is a more normal distribution than a distribution of scores, even when the population distribution is not normal.
what are the two principles of the central limit therom
Repeated sampling approximates a normal curve, even when the original population is not normally distributed.
A distribution of means is less variable than a distribution of individual scores.
distribution of means
s a distribution composed of many means that are calculated from all possible samples of a given size, all taken from the same population. also bell shaped andn unimodaler
what must we do with random sampling in tha distribution of means
replacment
What happens to the spread when we create a distribution of means rather that a distribution of scores
the spread decrease when we create a distribution of means rather than a distribution of scores
Why
But when we plotted means, we averaged that extreme score with two other scores. So each time we pulled a score in the 70s, we tended to pull two lower scores as well;
What happens to the standard deviation in a distribution of means verse a distribution of scores
A distribution of means has the same mean as a distribution of scores from the same population, but a smaller standard deviation.
what is the distribution of means symbol
The standard deviation symbol?
uses the symbol ?M
The symbol is ?M
what is the name for the standard deviation of a distribution of means.
standard error
whats happens as we increase the smaple sizes in a distribution of meansAs we've noted, the larger the sample size, the narrower the distribution of means and the smaller the standard deviation of the distribution of means�
As we've noted, the larger the sample size, the narrower the distribution of means and the smaller the standard deviation of the distribution of means�
When a population of scores in not normall distributed will it be normal? Why
ven if the population of individual scores is not normally distributed, the distribution of means will approximate the normal curve if the samples are composed of at least 30 scores.
AS a sample increases what happens to mean of a distribution of means
remains the same.
differnce bettwe standard deviation and standard error
Standard deviation is the measure of spread for a distribution of scores in a single sample or in a population of scores. Standard error is the standard deviation (or measure of spread) in a distribution of means of all possible samples of a given size fr
What does a z statistic�a z score based on a distribution of means�tell us about a sample mean?
The z statistic tells us how many standard errors a sample mean is from the population mean.
assumptions
are the characteristics that we ideally require the population from which we are sampling to have so that we can make accurate inferences.
differences between parametic and nonparametic
parametric tests, inferential statistical analyses based on a set of assumptions about the population. By contrast, nonparametric tests are inferential statistical analyses that are not based on a set of assumptions about the population.
critical values
critical values, the test statistic values beyond which we reject the null hypothesis.
critical region
critical region refers to the area in the tails of the comparison distribution in which the null hypothesis can be rejected.
p values
he probabilities used to determine the critical values, or cutoffs, in hypothesis testing are p levels (also often called alphas).
sstatistic signig
statistically significant if the data differ from what we would expect by chance if there were, in fact, no actual difference. T
one tail
one-tailed test is a hypothesis test in which the research hypothesis is directional, positing either a mean decrease or a mean increase in the dependent variable, but not both, as a result of the independent variable. rare in stats
two tail
A two-tailed test is a hypothesis test in which the research hypothesis does not indicate a direction of the mean difference or change in the dependent variable, but merely indicates that there will be a mean difference