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Flashcards in Quiz 1 Deck (56):
1

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.

51

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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1-Alpha (goes after type 1 error)

Probability of not rejecting the null hypothesis when in fact it's true