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84 Cards in this Set
- Front
- Back
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What is a nominal scale?
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A nominal scale is a set of categories that have no numerical order
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What is an ordinal scale?
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An ordinal scale is a set of categories that have a numerical order (i.e., the categories can be ranked) but the distance between categories is not equal.
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What is an interval scale?
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An interval scale is a set of ordered categories like an ordinal scale with the additional requirement that the numerical distance between categories is equal.
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What feature distinguishes a ratio scale from an interval scale?
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A ratio scale has an absolute zero (i.e., the point at which there is none of the quantity being measured).
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What is a population?
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The entire set of participants (or objects) that are of interest to the research question.
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What is a sample?
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A subset of individuals intended to represent a population.
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What do we call descriptive characteristics of a population?
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Parameters
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What do we call descriptive characteristics of a sample?
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Statistics
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Define Central Tendency
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Central Tendency is a statistical measure that identifies a single score as a representative for an entire distribution or set of data.
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. Define "mean."
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The mean is the average score in a distribution
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Define "mode."
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The mode is the most frequently occurring score in a distribution
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Define "median."
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The median is the midpoint of the distribution.
Another good answer: The score that half of the scores in the distribution are above and half are below |
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What is the only measure of central tendency that can be used for a nominal scale?
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Mode
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What types of central tendency can be used for an ordinal scale?
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Mode and Median
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For which types of scales can the mean be used?
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Interval and Ratio
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What does bimodal mean?
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The distribution has 2 modes
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In a positively skewed distribution, which is higher, the mean or the median?
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The mean (NOTE: The mean is always closer than the median to the tail of a skewed distribution.)
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What is the best measure of central tendency for a skewed distribution?
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The median
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Why is the mean a poor measure of central tendency for a skewed distribution?
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A skewed distribution has outliers in the tail. Outliers can make the mean unrepresentative of the distribution as a whole.
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What is the best measure of central tendency for a skewed distribution?
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The median
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Why is the mean a poor measure of central tendency for a skewed distribution?
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A skewed distribution has outliers in the tail. Outliers can make the mean unrepresentative of the distribution as a whole.
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If many samples are selected at random from the same population, which measure of central tendency is likely to be the most stable from sample to sample?
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The mean
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If many samples are selected at random from the same population, which measure of central tendency is likely to be the least stable from sample to sample?
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The mode
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Define variability.
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Variability is a measure of the degree to which scores in a distribution are spread out or clustered together.
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Define outlier.
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Outliers are extreme scores in a distribution.
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Name 3 reasons why measures of variability are important.
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Here are good answers:
1.They help us identify outliers. 2.They tell us how well the measure of central tendency summarizes the entire distribution. 3. They are used to compute other statistics. 4.They can be theoretically important in and of themselves |
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Define range
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The range is the difference between the highest score and the lowest score in the distribution.
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Name 2 disadvantages of using the range as a measure of variability.
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1.It does not take into account the variability of all of the scores in the distribution.
2.It is extremely sensitive to outliers. |
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Define variance.
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Variance is the mean squared deviation from the mean of the distribution.
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Why is the formula for variance different depending on whether the distribution is a population or a sample?
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Using the same formula would mean that the sample variance would underestimate the population variance. The slightly different formula corrects the underestimation.
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Define standard deviation.
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The standard deviation is the typical distance of a set of scores from their mean.
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What is the relationship between the standard deviation and variance?
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The standard deviation is the square root of the variance.
Another answer: The variance is the standard deviation squared. |
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Name 2 advantages of using the standard deviation instead of the range as a measure of variability.
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1. All of the scores in the distribution are used to calculate it.
2. It is less sensitive to outliers. (NOTE: The standard deviation is still sensitive to outliers, just not as much as the range |
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Define z-score
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A z-score is a standard score that indicates how many standard deviations a raw score deviates from the mean
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What is the mean and standard deviation of a set of z-scores?
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The mean is 0 and the standard deviation is 1.
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Define correlation coefficient
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The correlation coefficient is a statistic used to measure the linear relationship between 2 variables. (NOTE: A fully correct answer would have to include the word "linear.")
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A professor mentions in lecture that income and vocabulary ability have a correlation coefficient of 3.2. What is the proper thing to do?
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Stand up and denounce the professor as a fraud. Shout as loud as you can, "You FOOL! Don't you know that the correlation coefficient has a range of -1 to 1 and that values outside that range are IMPOSSIBLE?!!!!"
Okay, maybe that's a bit dramatic. Maybe just inform the professor later that there must be some mistake because correlations can only range from -1 to 1. |
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If the correlation between achievement motivation and actual income earned is 0, what can we conclude about the relationship between these 2 variables?
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They do not have a linear relationship
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If violent behavior and anxiety are negatively correlated, are highly violent people more likely to be anxious than less violent people?
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No.
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If income and happiness are positively correlated, describe 3 possible patterns of how income and happiness are causally related.
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1.Higher income causes people to be happier.
2.Increased happiness causes people to earn more money. 3.Another variable causes both higher income and increased happiness |
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If the correlation between variables X and Y is .45, what is the correlation between Y and X?
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.45
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Pretend that a researcher finds that the correlation between height and number of baskets per game for NBA starting players is very low. The researcher announces that height confers little advantage in the sport of basketball. Assume that the researcher's conclusion is not correct. Why might the researcher have obtained such a low correlation?
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Any time there is a restriction of range in 1 or both variables, the correlation might be misleading. In this case, almost all players are in the NBA are very tall. If the NBA included very short players, the correlation would probably be much higher.
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A researcher found that, in a sample of children and teenagers, vocabulary knowledge is highly correlated with age. The researcher concludes that because vocabulary is correlated with age, elderly people must have the best vocabulary. What is wrong with this conclusion?
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It is improper to generalize a conclusion beyond the ranges that were sampled (e.g., Just because age and vocabulary are correlated in teenagers does not necessarily mean that they are correlated at other age ranges.).
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A researcher found that in her small sample of 10 people, the 2 variables that she hypothesized would correlate, were not correlated at all. She decides to include 1 more person in the sample. Now, with 11 people, the 2 variables were highly correlated. Why should this researcher not trust her results?
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The 11thperson was probably an outlier, possibly yielding misleading results.
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Define regression
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Regression is a statistical procedure that finds the best fitting line through a set of data.
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In the regression equation (Y = b0 + b1X), what does b1 represent?
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The slope of the best fitting line in the scatterplot of X and Y.
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In the regression equation (Y = b0 + b1X), what does b0 represent?
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The Y-intercept of the best fitting line in the scatterplot of X and Y.
Another answer: The estimated value of Y when X equals 0. |
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In regression, for any particular value of X, what do we call the difference between Y and the predicted value of Y (Y-hat)?
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Error
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What do we call the typical distance between the observed Y values and the regression line?
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The standard error of the estimate.
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If IQ explains 36% of the variance in Academic Achievement, what is the correlation between IQ and Academic Achievement? (Assume that the correlation is positive.)
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0.6 (NOTE: The percentage of variance explained equals the correlation coefficient squared.)
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If the correlation between the personality trait of psychopathy (i.e., gross violations of the basic rights of others coupled with the inability to feel remorse) and anxiety is -0.35. What percentage of the variance in psychopathy is explained by anxiety?
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12.25% (NOTE: The percentage of variance explained equals the correlation coefficient squared.)
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What is the Gambler's Fallacy?
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It is the incorrect belief that in a sequence of independent random events (e.g., coin tosses), the probability of 1 event is changed by the outcomes of the preceding events.
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What is the distinction between descriptive and inferential statistics?
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Descriptive statistics summarize tendencies and characteristics of data. Inferential statistics use sample statistics to make inferences about the populations from which the samples were drawn. Inferential statistics are used for hypothesis testing.
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Define the distribution of sample means.
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The distribution of sample means is the collection of sample means for all the possible random samples of a particular size (n) that can be obtained from a population
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Under what conditions will the distribution of sample means be normal?
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1. If the original population is normal.
or 2. If the sample size n > 30 |
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Under what conditions will the distribution of sample means be normal?
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1. If the original population is normal.
or 2. If the sample size n > 30 |
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If a population has a mean of μ = 12, what will the mean of the distribution of sample means be?
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12
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Which is bigger, the standard deviation of a population or the standard deviation of the distribution of sample means drawn from that population (assuming that n > 1)?
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The standard deviation of the population.
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Which is bigger, the standard deviation of a population or the standard deviation of the distribution of sample means drawn from that population (assuming that n > 1)?
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The standard deviation of the population.
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What is another name for the standard deviation of the distribution of sample means?
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The standard error of the mean
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What does the Central Limit Theorem tell us?
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For any population with mean μ and standard deviation σ, the distribution of sample means for sample size n will approach a normal distribution with a mean of μ and a standard deviation of σ / sqrt(n) as n approaches infinity.
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A hypothesis test is a test of the
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a) null hypothesis (H0)
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What is the alternative hypothesis?
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The hypothesis the researcher believes to be true.
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The null hypothesis is false and you rejected it. You’ve made a…
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a) Correct decision
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Your research led you to report that Skippy Peanut Butter causes AIDS. In reality, it doesn’t. You’ve made a…
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type 1 error
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You hypothesized that a certain variable has an effect. In truth, it really does have an effect. You retained the null hypothesis. You’ve made a…
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type 2 error
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The null hypothesis is false. You retained it. You’ve made a…
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type 2 error
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The null hypothesis is true. You retained it. You’ve made a…
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a) Correct decision
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The null hypothesis is true. You rejected it. You’ve made a…
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type 1 error
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You report that there is no evidence that testosterone levels increase aggression. Did you retain the null hypothesis?
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yes
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If α is high, am I more likely to make a Type I error?
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yes
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In statistics, β is the probability of..
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making a Type II error when the null hypothesis is false.
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The symbol for the probability of making a Type I error when the null hypothesis is true is...
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α
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The probability of correctly rejecting a null hypothesis that is false is called...
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Statistical power
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Increasing sample size will...
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increase power
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Increasing α will...
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increase power.
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Provided that you correctly specify the direction of an effect, a 1-tailed hypothesis is more powerful than a 2-tailed hypothesis.
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true
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What kind of estimate is most likely to be correct?
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interval estimate
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Define a confidence interval
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An interval estimate that is calculated to contain the population parameter a certain percentage of the time.
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Define margin of error
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The distance from the point estimate to the upper bound (or lower bound) of a confidence interval
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what does cohens d measure?
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the distance between two mean in standard deviation units.
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When should you reject the null hypothesis?
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When p is less than .05
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What are the assumptions made in t tests?
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Normality- the distribution of the sample mean is normal
Homogenity of variance-The variablity of a sample is approximetly the same as the variablitity of the population Independence-the probabilty of a score does not depend on the past scores drawm. |
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Why is a z test better than a t test?
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a z test uses population standard error while t test uses estimated standard error. There a t test is more accurate.
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