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1. What is the purpose of descriptive statistics? Give examples
Statistical procedures used to summarize, organize, and simplify data. Taking raw scores and organizing/summarizing them into a more manageable form.
1. What is the difference between a population and a sample?
Population includes all the individuals of interest in a particular study. A sample is a subset of individuals selected from a population to use in a research study. You use data from a sample to generalize the population
1. What is meant by random selection? Why is it important?
Selecting people randomly from the population to be in the sample. Probability comes into account, we want the probability to remain the same for each individual—sample with replacement!
1. What is the purpose of inferential statistics?
Inferential statistics consists of techniques that allow us to study examples and then make generalization about the populations from which they were selected. Samples are representative of their populations.
1. What is random assignment? Why might it be considered more important than random selection?
Each participant has an = chance of being assigned to each treatment condition distributing characteristics evenly between the 2 groups so that no group is noticeably dominant than the other.Random assignment is more feasible, and more convenient
--gets rid of confounds -> representative of the population
-- take Madison students rather than all university students in the world.
Sampling error is the discrepancy, or amount of error, which exists between a sample statistic and the corresponding population parameter. Samples don’t usually match the population. Discrepancy of inferential statistics.
1. Be able to identify independent and dependent variables
Independent variables are manipulated by the researcher. Dependent variables are observed in order to assess the effect of the treatment.
1. What are confounds and what are some ways to minimize them?
Confounds are variables not intended to have an influence, but might get in the way. By controlled conditions, one can minimize the effects of confounds.
--random assignment (best way)
1. What is the difference between true experiments, quasi-experiments, and correlation studies? What are the advantages and disadvantages of each and when would each be used?
have manipulated variables and methods of control. Control and experimental conditions; dependent and independent variables; confound variables.
Quasi-experiment: comparison of naturally existing groups (gender, culture…). No manipulation. Cannot determine causation.
1. What are the key features of nominal, ordinal, interval, and ratio data? Be able to recognize and give examples of each measurement scale. What advantages are associated with each?
Nominal: can be named, have no value
--gender, hair color…
Ordinal: ranks, different intervals between numbers
Interval: equal intervals between values, no absolute zero (0 doesn’t mean no heat)
Ratio: interval scale with absolute zero. (0 inches does mean no height)
1. What is an operational definition and why is it important?
it identifies a measurement procedure for measuring an external behavior.
uses resulting info as definition of hypothetical construct.
1. What are the best ways to organize data? When would you use a bar graph or a histogram? How do you organize data in a frequency table? When would your frequency table be grouped or ungrouped?
Nominal data: bar graph, bars don’t touch
Ordinal data: bar graph, bars don’t touch
Interval/ratio data: histogram, ungrouped, continuous—bars touch
Frequency table: frequency, cumulative frequency, cumulative percentage; proportions and percentage can be included as a separate column. Grouped frequency for continuous data—use real limits (boundaries of intervals for scores measured on a continuous number line)—bars touch.
1. What is the difference between centile point and centile ranks? Why would we use them?
Centile rank inticates % of people who score at or below that score. Converts raw score to percentile.
Centile point indicates the raw score associated with a certain percentile. Score at which a percentage of people scored at or below. Converts percentile to raw score.
1. What measurement scale corresponds to centile scores?
Ordinal. Intervals between the centiles are not the same; therefore, you can’t add/subtract them
1. Compare and contract mean, median, and mode as measures of central tendency. When should each be used?
Mean: averages of all scores
Median: middle number, not value-driven, based on counts
Mode: most common, nominal data
1. How do outliers affect the mean, median, and mode? What does it mean to be “value-driven” or “count-driven”?
An extreme score. Doesn’t affect the median or mode (dependent on count). Skews the mean because it is dependent on value.
Total distance below the mean=total distance above the mean. The mean can never be outside the range of scores.
1. What does it mean to be an “unbiased estimator?” give 2 examples.
m -> population mean
s -> standard deviation of population (don't forget n-1!)
1. Be able to recognize a skewed distribution. How and why does skew affect the mean, median, and mode?
Doesn’t affect the median or mode (dependent on count). Skews the mean because it is dependent on value. Positively skewed distribution, the peak is on the left side, mean>median. Negatively skewed, the peak is on the right side, mean<median.
1. What is the sum of squares? Why is it important?
Sum of the deviation scores. Needed to compute variance and standard deviation.
1. Contrast the range and the IQR. When is the IQR a better measure of variability?
Range= upper real limit—lower real limit. If integers, high score—low score
Range can be affected by outliers, IQR avoids that problem. Range of middle 50%.
1. What are deviation scores and how do we use them in calculating the standard deviation? Why do we have to square them?
Deviation: distance from the mean
Standard deviation: average distance for all data points from the mean
The sum of all deviation points will always equal zero. We need to get rid of the positive and negative numbers, since they cancel each other out---we square the deviances!
1. What are degrees of freedom? How do they relate to the standard deviation?
How many scores are free to vary. If you calculated the mean for 10 people’s scores and lost one, you could calculate the missing score. What if you lost 2? Therefore, df=n-1. Whenever a mean is calculated we lose 1 df.
1. Why do we divide by n-1 in the standard deviation formula? How would the standard deviation by biased if we didn’t divide by n-1?
Divide by n-1 because it is a sample formula. It corrects the bias in sample variability. The adjustment increases the value you will obtain, making the sample variance an accurate, unbiased, estimator of population variances.
1. What is the difference between the standard deviation and the variance? Which do we prefer and why?
Standard deviation is the square root of the variance. We prefer standard deviation because it is less biased.
1. Why do we have both a conceptual and a calculational formula for the standard deviation? When would you use each one?
Use the calculational formula for computations where there are many decimals. You don’t have to calculate the mean, therefore, you don’t have to round.
Conceptual formula deals with what is standard deviation? The distance from the mean
1. What advantages do the standard deviation and variance have over the range and IQR?
Standard deviation and variants are influenced by outliers. IOR is not influenced by outliers.
Standard deviation and variance uses all the numbers in the distribution.
Standard deviation and variance are unbiased!
1. What is a z-score? What are the advantages of using z-scores over raw scores?
Tell you the exact location of a score within a distribution, how many standard deviations a score is away from the mean. Z-scores are comparable to each other, scores from different distributions can be converted to z-scores.
1. What is probability and how does it relate to sampling? How does it relate to z-scores and the unit normal table?
For a situation which several possible outcomes are possible, the fraction or proportion of all the possible outcomes. The Unit Normal Table shows the proportion for z-scores, lists relationships between z-score locations and proportions in normal distribution.
1. What are some characteristics of the normal distribution? Why is it special?
Symmetrical, bell-shaped, mean=median=mode, point of inflection = +/- 1 standard deviation, extends to positive and negative infinity, may have different M and SD, in the population, expect certain% to fall in each segment
1. What is the unit normal table and how do you use it?
Lists proportions of the normal distribution for a full range of possible z-score values. Columns.
1. What measurement scales are z-scores and centiles? Why does it matter?
z-scores on interval scale (equidistant intervals), can be easily compared and meaningful combined. Centile is not equidistant, clustered near center, inextreme differences are exaggerated. Ordinal measurement scale, based on equal area under the curve.
1. Be comfortable in making conversions between raw scores, centiles, z-scores, and transformed scores, in any direction.
Probability à z-scores à x score
x-score à z-score à probability
probability <-> z-score use Unit Normal Table
x-score <-> z-score use formula
1. What is sampling distribution? What is the distribution of means?
Sampling distribution: distribution statistics obtained by selecting all the possible samples of a specific size from a population. The distribution means is the collection of all sample means for all the possible random samples of a particular size (n) that can be obtained from a population.
1. What is the standard error? How is it different from sampling error?
Variability of sample means measured by the standard deviation of sample scores. Sampling error is the discrepancy, or amount of error, which exists between a sample statistic and the corresponding population parameter. Samples don’t usually match the population. Discrepancy of inferential statistics.
Sampling error: the mean of the sample compared to actual population
1. Describe the central limit theorem and how it helps us to describe the shape, mean, and standard error of the distribution.
1. Distribution of sample means with have the mean of the population
2. Distribution of sample means will approach a normal distribution as n approaches infinity.
3. Distribution of sample means will have standard deviation of standard deviation/square root of n
1. Know how z-scores and the unit normal table to determine the probability that a sample mean came from the original population.
--Percentage for probability
--Decimal point for propartion
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