Statistics Essay
A. Statistics are often used to describe and interpret the results of
intelligence testing.
* Describe three measures of central tendency (mean, median, and
mode).
mean = adding all the values to get sum and then dividing by the total number of
values
median = middle of the data
mode = number that occurs the most
* Describe a skewed distribution.
set of data with an outlier that is different from most of the other data
* Relate the three measures of central tendency to a normal distribution.
mean, median, and mode will be the same
* Relate the three measures of central tendency to a positively skewed
distribution.
mean will be pulled to the positive standard deviation side of the distribution, the
mode will be toward the negative standard deviation side of the distribution, the
median will be in between the mean and mode.
* An intelligence test for which the scores are normally distributed has a
mean of 100 and a standard deviation of 15. Use this information to
describe how the scores are distributed.
68% of data will be between 85 (-1 SD) and 115 (+1 SD). 95% of data will be
between 70 and 130 ( +/- 2 SD).
* In two normal distributions, the means are 100 for group I and 115 for
group II. Can an individual in group I have a higher score than the mean
score for group II? Explain.
yes, because 50% of the values in group I are above 100 then some of them will
be greater than 115.
B. If the null hypothesis is that there is no difference between the means of
scores of group I and group II and the t-test for statistical significance at
the .05 critical value is tobt = 5.38 and the tcrit = 2.97, what can you
conclude about the differences between these two groups? What might
this say about how this study was conducted? Was the sample in each of
the groups representative of the population as a whole? What might
account for you answer?
Since tobt is greater than tcrit then the differences between the means of the
two groups is statistically significant. This means that the differences between the
means are less likely to be due to chance variations between the groups.
There was a large sample of people.
Yes, a larger sample size would increase the chances of a representative
sample of the population as a whole.
By using random selection from the population.