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PSC 202 Exam 2
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Terms in this set (50)
Formula for t-statistic
(observed stat. − expected value of stat)÷(standard error of statistic)
Steps for finding the standard error of a difference of means
1. Square the standard error for each mean
2. Sum these numbers
3. Take the square root of the sum
Cross-Tabulation
Used when all variables are
nominal-level or ordinal-level and compares frequencies across categories of independent variable.
Mean Comparison
Used when dependent
variable is interval-level; others are nominal- or ordinal-level.Compare means across categories of
independent variable.
After controlling for z, we can identify one of following types of relationships
Spurious, Additive, Interactive
Spurious relationship
a false association between two variables that is actually due to the effect of some third variable
Additive relationship
Multiple independent variables, each with its own individual impact on the dependent variable
Interactive relationship
The impact of one independent variable depends on the impact of another independent variable
One standard deviation
68%
Two standard deviations
95%
Z score formula
(observed x − mean of x)÷(standard deviation of x)
Z score
Converts raw deviations from population mean into standard units
Z table
Gives the proportion of observations that fall above the given value of Z.
sample
A relatively small proportion of people who are chosen in a survey so as to be representative of the whole.
population
(statistics) the entire aggregation of items from which samples can be drawn
random sampling error
An error that occurs because of change; statistical fluctuations in which repetitions of the basic experiment sometimes favour one experimental condition and somtimes the other
standard error
the typical deviation of our
estimate from the "truth" in repeated tests
null hypothesis
states that, in the population, there is no relationship between the dependent and independent variables, and any relationship observed in a sample was produced by random sapling error
t-distribution
A symmetrical, bell-shaped distribution that is contingent on sample size. It has a mean of zero and a standard deviation equal to 1
z-distribution
A special case of the normal distribution in which the mean equals zero and the standard deviation equals one. For more information about this term, see the Basic Statistics module.
Ha
Alternative hypothesis (our hypothesis)
Ho
Null hypothesis
Rule of ± 2
if t-statistic ≥ 2 or ≤ -2, we can
reject the null hypothesis
t-statistic
the number of standard errors
between our estimate and Ho
p-value
the probability of getting the data we
observed through random error if H0 is true
level of significance
the level of error we are
willing to tolerate when rejecting H0
Pearson's r
A standardized measure of the strength of relationship between variables. It can take any value from - 1 (as one variable changes, the other changes in the opposite direction by the same amount) through 0 (as one variable changes, the other doesn't change at all), to + 1 (as one variable changes, the other changes in the same direction by the same amount).
Multiple Regression Equation
y = a + b1 · x + b2 · z
dummy variable
can only take on the value of 1 or 0, allow for assessment of nominal and ordinal independent variables in regression equations as interval level
Regression Analysis
Estimates the direction and size of the effect of the independent variable(s) on the dependent variable and fits the dependent variable as a linear function of the independent variable(s)
μ
Population mean
N
Population size
σ
Population standard deviation
"X bar"
Sample mean
n
sample size
s
sample standard deviation
standard error of the sample mean
Measures how much the sample mean departs by chance, from population mean
95 percent confidence interval
The interval in which 95 percent of all possible values of sample mean will fall by chance
standard error of a sample proportion
Measures how much p (proportion of a sample falling into one value of a nominal or ordinal variable) departs, by chance, from a population proportion
p
proportion of a sample falling into one value of a nominal or ordinal variable
q
proportion of a sample falling into all other values of a nominal or ordinal variable
test of statistical significance
helps you decide whether the observed relationship between an independent variable and a dependent variable really exists in the population or whether it could have happened by chance when the sample was drawn
measure of association
tells the researcher how well the independent variable works in explaining the dependent variable
Type I error
Occurs when the researcher concludes that there is a relationship in the population when in fact there is none
Type II error
Occurs when the researcher infers that there is no relationship in the population when in fact there is
.05 level of significance
If there is a plausible likelihood (more than 5% of the time) that random sampling error produced the relationship we see in the sample, we do NOT reject the null hypothesis.
standard error of the mean
is equal to the standard deviation divided by the square root of n, s/√n
standard error of the difference
1. Square each mean's standard error.
2. Sum the squared standard errors
3. Take the square root of the sum obtained in step 2
confidence interval approach
when the investigator use the standard error the determine the smallest plausible mean difference in the population, if it is greater than 0 the null hypothesis can be rejected
P-value approach
the researcher determines the exact probability that of obtaining the observed sample difference , under the assumption that the null hypothesis is correct. if the P-value is less than or equal to .05 then the null hypothesis can be rejected
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