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Terms in this set (30)
population
larger group to which results are generalized; aggregate of persons, objects, or events that meet specified set of criteria
sample
a subgroup of the population that serves as the reference group
sampling bias
when the individuals selected for a sample over- or under-represent certain population attributes
Descriptive statistics
to categorize the shape, central tendency, and variability within a data set
parameters
measures of population characteristics
statistics
descriptive indices computed from sampled data
(the characteristics of interest of my sample)
examples of different measures of dispersion
range
percentiles/quartiles
variance
standard deviation
coefficient of variation
basic elements of descriptive analysis
- frequency of the distribution(s)
- shape of the distribution(s)
- measures of central tendency
- measures of dispersion
distribution
the total set of scores recorded for a particular set of variables
the frequency of the distribution
a table or graph format intended to show the number of occurrences of a score
inferential statistics
tells us with a certain degree of uncertainty how our sample stats relate back to the population
Median
the value indicating that there are as many scores above and below it (50% mark)
mean
the value indicating the sum of scores divided by the number of scores composing the dataset
only index subject to arithmetic manipulation
measures of dispersion
provides an accurate description of how the scores are dispersed within the data set
range, %iles, variance, SD, coefficient of variation
range
the difference between the max and min scores
Percentile
an index used to describe a score position within the distribution
--> divides the data into 100 equal portions and a particular score is located in one of these portions, which represents its position relative to all other scores
standard deviation
measures the typical distance between each data point and the mean (the spread of the data distribution)
Variance
the average of the squared differences from the mean
provides an index that reflects the variation within the full data set
the limitation of variance is in it's final unit (squared)
coefficient of variation
a ration of the standard deviation - becomes practical to compare distributions from samples with different units
hypothesis testing
inferential statistics used to answer questions concerning comparisons or relationships
should be a simple yes/no question!
Null hypothesis (H₀)
mean of treatment group (pre) = mean of treatment group (post)
Alternative hypothesis (H₁)
mean of treatment group (pre) ≠ mean of treatment group (post)
two situations in which the decision can be wrong as it pertains to statistical data and hypotheses
the null hypothesis may be true, whereas we reject (H₀)
the alternative hypothesis may be true, whereas we do NOT reject (H₀)
parametrical analysis
assumes that the sample data comes from a population that can be adequately modeled by a probability distribution that has a fixed set of parameters
interquartile range (IQR)
a measure of statistical dispersion, being equal to the difference between 75th and 25th percentiles, or between upper and lower quartiles,
IQR = Q3 − Q1
type I statistical error
false positive - reject the true null hypothesis
"convict an innocent defendant"
type II statistical error
false negative - fail to reject a false null hypothesis
"acquit a criminal"
variance vs standard deviation
Variance represents all data points in a set and is calculated by averaging the squared deviation of each mean
standard deviation is a measure of spread around the mean when the central tendency is calculated via the mean
Variance helps to find the distribution of data in a population from a mean, and standard deviation also helps to know the distribution of data in population, but standard deviation gives more clarity about the deviation of data from a mean
effect size
the magnitude of the result as it occurs, or would be found, in nature, or in a population
statistical power
the likelihood that a study will detect an effect when there is an effect to be detected
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Verified questions
PROBABILITY
Suppose that $$ 10^6 $$ people arrive at a service station at times that are independent random variables, each of which is uniformly distributed over $$ \left( 0,10 ^ { 6 } \right) $$ . Let N denote the number that arrive in the first hour. Find an approximation for P{N=i}.
STATISTICS
Use these results from a USA Today survey in which 510 people chose to respond to this question that was posted on the USA Today website: "Should Americans replace passwords with biometric security (fingerprints, etc)?" Among the respondents, 53% said "yes." We want to test the claim that more than half of the population believes that passwords should be replaced with biometric security. Identify the actual number of respondents who answered "yes."
STATISTICS
Use the following list of ingredients for chocolate brownies to solve. Ingredients for 16 Brownies. $\frac{2}{3}$ cup butter, 5 ounces unsweetened chocolate, $1 \frac{1}{2}$ cups sugar, 2 teaspoons vanilla, 2 eggs, 1 cup flour. How much of each ingredient is needed to make 24 brownies?
QUESTION
The Harvard College Alcohol Study finds that 67% of college students support efforts to "crack down on underage drinking." Does this result hold at a large local college? To find out, college administrators survey an SRS of 100 students and find that 62 support a crackdown on underage drinking. A writer in the college's student paper says that "support for a crackdown is lower at our school than nationally." Write a short letter to the editor explaining why the survey does not support this conclusion.