What is the difference between measures of central tendency and variation?
statistics
Description
1- What is the
difference between measures of central tendency and variation?
Central
tendency includes the mode, median and mean, and the mean can only be used with
interval/ratio data. These are measures of data around a central value.
Variation refers the diversity in a given distribution, known as measures of
variability. These include variance, standard deviation, interquartile range
and range.
2- If the standard
deviation of a set of scores is equal to 2, what will the variance be? And if
there are 16 scores in that set, what will be the standard error of the mean?
3- What is the
difference between nominal and ordinal levels of measurement? Give an example
for each of them.
Nominal
scales apply labels to variables without a quantitative value. Examples would
be gender (a dichotomy) or hair colour. Ordinal scales are the order of values
according to significance or importance.
A 5 point Likert scale, from extremely unsatisfied to extremely
satisfied would be an example.
4- A researcher
reported that the null hypothesis at the 5% level of significance was rejected.
What does it mean in plain language?
It means
that at a 95% level of confidence, you could say that an alternative hypothesis
of a dependent relationship between variables exists.
5- How important is
the p-value score in interpretation of the results?
The
p-value or probability value is used in null hypothesis testing to measure
statistical significance. The threshold value for p is usually set at 5% or 1%,
called the significance value. In interpreting results, it is very important,
as it shows if the result is statistically significant (rejection of the null
hypothesis).
6- IQ scores have a
normal distribution with a mean of 100 and a standard deviation of 15. What
percent of people have an IQ above 120? .909
7- Suppose a
researcher measures the results of a treatment in two different groups and
would like to compare them. Should the researcher use an independent samples
t-test or a correlated samples t-test to compare the two sets of scores?
8- If a researcher
uses a paired t-test, and if the degree of freedom (df) for the t-test is equal
to 86, how many participants were in the study?
9- When should post
hoc comparisons be performed and why?
