Chapter 13 (Lila) Flashcards
normal curve (often known as the bell-shaped curve)
The normal curve is bilaterally symmetrical; its shape is identical to the left and right of the mean (the highest point on the curve).
• As a consequence, the mode, the median, and the mean of the normal curve are all equal.
• The tails of the normal curve are asymptotic, which means they approach but never quite meet the horizontal axis. As a consequence, any value can be placed u
Normal distribution
the frequency distributions associated with normal curves) that they contain share a number of characteristics:
central-limit theorem
states that “regardless of the shape or form of a population distribution, the distributions of both the sum and the mean of random samples [taken from that population] approach that of a normal distribution as the sample size is increased”
statistical significance
on tests that allow us to assess whether sample statistics are acceptable estimates of population parameters
Type I error
is when we infer that a relationship found in the sample exists in the population when in fact it does not (a false positive)
Type II error
is when we do not find a relationship within the sample data and infer that there is not a relationship within the population when in fact there is (a false negative).
Chi-square
Chi-square tests the independence of two variables by assessing the likelihood that the relationship observed in the sample is due to chance. In other words, the test asks, “What is the probability that the relationship does not exist in the population?” As a non-parametric statistic, it allows researchers to test relationships among nominal and ordinal variables. Chi-square also has the distinct advantage of being a highly stable measure, one based on a cell-by-cell comparison of the observed relationship and the expected relationship under the null hypothesis. We can state the null and research hypotheses of chi-square as follows:
H0: fo = fe
H1: fo ≠ fe
In this formula, fO is observed frequencies and fe is expected frequencies.
difference of means
. Significantly different means suggest a relationship between the interval/ratio variable and the nominal or ordinal variable that the subgroups are based on.
two-tailed test.
the direction of the difference is not important to us, we use what is called a two-tailed test.
one-tailed test.
If the direction of difference does matter to our theory—the two former assumptions—we use a one-tailed test.
the control variable.
A Bivariate Causal Relationship
To contemplate the effects of a third variable, we must control for that variable. To do this, we look at the relationship between our independent variable A and our dependent variable B while holding constant values of variable C, and then consider what happens to the relationship between A and B for each value of variable C. If we are controlling for gender, for example, we would be interested in the relationship between A and B for men only and for women only. To do so, we would conduct separate analyses for men and women and then examine the form/direction, strength, and statistical significance of the relationship between A and B for men and women. The variable being controlled is referred to as the control variable.
