Flashcards in Quiz 1 Deck (56):
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State Central Limit Theorem
-CLT
-Given a population with finite mean u (mew) and finite variance O^2 (sigma squared), the sampling distribution of the mean approaches a normal distribution with mean u and variance O^2/N, as N, the sampling size, increases
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Statistic
-Quantity calculated from a sample
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Population
-Set of all objects that we’re interested in researching
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Parameter
-Quantity calculated from a population
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Significance
-Unlikely to have occurred by chance alone
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Sample
-Subset of a population
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Random Sample
-Each member of a population has equal likelihood of being chosen
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X-bar
_
X
-Sample mean
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S^2
-Sample variance
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S
-Sample standard deviation
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U (mew)
-Population mean
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O^2 (sigma squared)
-Population variance
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O (sigma)
-Population standard deviation
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Descriptive Statistics
-Numbers that summarize or describing data
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Inferential Statistics
-More in terms of hypothesis testing
-Allow us to test hypotheses about the differences between groups on the variable being measured
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Measures of Central Tendency
-Mean: arithmetic average
-Median: middlemost score
-Mode: most frequently occurring score
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Measures of Dispersion
-Range
-Standard Deviation
-Variance
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Range
-Largest score - Smallest score
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Variance
-Average of square deviation about (from) the mean
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Standard Deviation
-Square root of variance
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Types of Frequency Distributions
-Leptokurtosis
-Platykurtosis
-Normality
-Skew
-Kurtosis
-Bimodal
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Kurtosis
-The peakedness or flatness around the mode of a frequency distribution
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Leptokurtosis
-More scores in the tails and fewer scores in the middle as compared to the corresponding normal distribution
-Tends to happen more in smaller samples
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Platykurtosis
-Fewer scores in the tails and more scores in the middle as compared to the corresponding normal distribution
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Normality (Normal Distribution)
-The left and right sides look alike (if you split the graph down the middle)
-a.k.a. Bell curve or Gaussian distribution
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Skew
-Refers to the amount of asymmetry of the distribution
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Positively Skewed
-Vast majority of the data is on the left (or low side) of the tail
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Negatively Skewed
-Vast majority of the data is on the right (or high side) and the tail is pointing to the left
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Frequency Polygon
-Shows the distribution of subjects scoring among various intervals
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Histogram
-A graphical representation of the data using bars
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Bar Chart
-When the x-axis is categorical in nature
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Bimodal Distributions
-Most common distribution found in psychology
-Two humps
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Sampling Distribution
-A distribution under repeated sampling and equal-sized samples of any statistic
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Z-Scores
-Statistic that allows us to determine how far we are away from the mean
-a.k.a. Standard scores
-Determine how far away scores are from the mean in standard deviational units
-May be both descriptive and inferential
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Characteristics of standard normal distribution
-Has a mean (or u) or 0
-Has standard deviation (or o (theta)) of 1
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Confidence Interval
-A 95%, 99% (or some stated) probability that the interval falls around (or about) the parameter (u)
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df
-Degree of freedom (independent piece of information)
-Can change, but for confidence interval, it will be N-1
-If N>/= 100, use infinity
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T-Distribution
-William Gosset
-Is leptokurtic, and as you increase the sample size, it becomes normal, such that t(sub infinity)=z
-Kate Moss
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Standard Error
-Standard deviation of a sampling distribution
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Hypothesis
-Educated guess about which group will be significantly higher on a measure or if there will be a positive or negative relationship between two measurements
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Independent Variable
-A variable that is manipulated by the experimenter
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Dependent Variable
-A variable that is measured
-A score
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Null Hypothesis
-Ho (that’s a sub o)
-”Null” means “no”
-No difference in rates, scores, etc.
-No statistically significant difference between or among population means on a particular measurement
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Type I Error
-Probability of rejecting the null hypothesis when in fact it’s true
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Type II Error
-Inability of detecting a difference if in fact one exists
-Insensitivity of experiment
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Power
-Ability to detect a difference if in fact one exists
-Sensitivity of the experimentsp
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Determinants of Alpha
-(fishy looking thing)
-1. Experimenter
-2. Journal Editors
-We usually set our alpha = .05
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Determinants of Power
-Power and B go opposite
-Look in notes
-1. N goes up, Power goes up, B goes down
-2. O^2 goes up, Power goes down, B goes up
-3. Skew goes up, Power goes down, B goes up
-4. Outliers go up, Power goes down, B goes up
-5. Difference between group means go up, Power goes up, B goes down
-6. Alpha goes up, Power goes up, B goes down
-7. One vs. Two-Tailed Tests: 1 tail (more power); 2 tail (less power)
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Heuristic Formula of F (in words)
# of folks in a group x(times) variance among group members/ average variance within groups
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Is the F-Ratio that you compute larger than the critical value in the table? (Conclusion).
-If yes, statistically significant. Group A is significantly higher than Group B on the dv.
-p < .05; p< .01
-If no, not statistically significant (nonsignificant). There is no statistically significant difference between Group A and Group B on the dv.
-p > .05; n.s.
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Assumptions of ANOVA. Why Fisher made them?
-1. Normality in the Population
-a. That’s how Fisher derived out the critical values of F
-b. From CLT, the sampling distribution of the mean approaches normality as N increases
-Kolmogorov-Smirnov
-Shapiro-Wilk’s W=1.0
2. Homogeneity (homoscedasticity) of Variance in the Population
O(sub 1)^2 = O(sub 2)^2 = O(sub 3)^2
-Why? Fisher averaged “like commodities” (sample within variation) to obtain his best estimate of O^2 from O^2/N
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What happens when you violate the assumptions?
-1. Robust = when you violate the assumption, the Type I error rate doesn’t change appreciably from the normal level. (stated)
-2. Liberal = when you violate the assumption, the Type I error rate is higher than the nominal level
-We don’t like these tests
3. Conservative = when you violate the assumption, Type I error rate is lower than the stated level
-When you violate these assumptions? It is still robust
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Characteristics of F
-1. F distribution is positively skewed
-2. X-bar(sub F) = df(sub w)/df(sub w) -2
-3. F (sub infinity), infinity = always 1.00
-Any ration below 1.00 will be nonsignificant
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Correlation Factor
-Takes the raw data and converts it into deviational scores
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Is the t value that you compute higher than the critical value in the table? (Determinants of Alpha).
LOOK IN PACKET
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