Psych Stats: Normal Dist., Z-scores, Hypothesis Testing, & Effect Size, Exams of Psychology

Download Psych Stats: Normal Dist., Z-scores, Hypothesis Testing, & Effect Size and more Exams Psychology in PDF only on Docsity! Psychological Statistics Exam 2 The Normal Distribution - -unimodal -symmetric -mathematically defined (shape has equation) -theoretical Big Five Traits ("OCEAN") - usually fit normal curve -Openness -Conscientiousness -Extraversion - high = very social; low = enjoys time alone -Agreeable -Neuroticism - high = stressed reactive, depression, anxiety - low = nothing bothers you - still a problem As your sample size ______, shape of distribution will more closely resemble the ______. As long as the underlying population distribution is ______ - 1. increases 2. the normal curve 3. normal Standardization - - Allows for comparisons across different measurement scales - Converts individual scores (from different normal distributions) to a shared normal distribution Z-score - Numerical value of a z-score specifies the distance (# of SD) that a value is above or below the mean Standard normal distribution - A normal distribution of z-scores Z- distribution - - The normal distribution of standardized scores mean (μ) = 0 SD (σ) = 1 If z = 1 then your value is 1 SD above the mean If z = -2 then your value is 2 SD below the mean What does the z-distribtuion allow us to do? - 1. Transform raw scores to z scores (standard scores) 2. Transfrom z scores into raw scores 3. Compare z scores to each other - even if the raw scores are measured on different scales 4. Transform z scores into percentiles Transforming raw scores --> z-scores - 1) subtract the population mean (μ) from the raw score (X) 2) Divide by the population SD (σ) z = (X-μ)/σ Transforming z-scores --> raw scores - 1) Multiple the z-score by the population SD (σ) 1. Convert a raw score into a z score 2. Look up given z score on the z table to find the percentage of scores between the mean and that z score If its a positive z-score - add it to 50% If its a negative z-score - subtract from 50% Hypothesis Testing - We test a hypothesis by determining the likelihood that a sample statistic would be selected if the hypothesis regarding the population parameter were true Parametric Tests - Inferential statistical analyses based on a set of assumptions about the population - requires assumptions about the population Assumptions - the criteria that are met, ideally, before a hypothesis is conducted Robust hypothesis test - One that produces valid results even when all assumptions are not met Assumptions or Conducting Analyses (Parametric Tests) - 1. The Dependent Variable is assessed using a scale measure (cannot be nominal or ordinal) 2. Participants are randomly selected 3. The distribution of the population of interest must be approximately normal Hypothesis testing with Z tests - 1. State the hypothesis 2. Set criteria for a decision 3. Compute the test statistics 4. Make a decision 1. Stating the Hypothesis - Null = Ho Alternative = H1 Null hypothesis - the hypothesis that there is no significant difference between specified populations, any observed difference being due to sampling or experimental error Alternative Hypothesis - the hypothesis that sample observations are influenced by some non-random cause 2. Setting the Criteria - 1. Critical Values 2. Critical Regions 3. Significance Testing Critical Values - test statistic values beyond which we reject the null hypothesis "cut off values" Critical Regions - the area in the tails of the distribution in which the null hypothesis will be rejected Significance Testing - significance level or alpha level (α level) = highest probable value taken as evidence against the null hypothesis - p-value: probability of obtaining sample values when the null hypothesis is true - low = good - high = bad 3. Computing the test statistic - Compute and then compare an inferential test statistics to the critical values - Z statistic can be used when the population mean and population SD are known - If a test gives a p-value lower than the significance level (α level), - the null hypothesis is rejected, and the results are "statistically significant". - The lower the α level chosen, the stronger the evidence required 4. Making a decision - - Does the s statistic fall in the critical regions? - Does is exceed the critical values? Non-directional (2-tailed) tests - Used to test hypotheses when we are interested in *any* alternative to the null hypothesis - The research hypothesis does not indicate a direction of the mean difference or change in the DV, but merely indicates that there will be a difference ex. Ho: μ=100 H1: μ =/= 100 Directional (1 tailed) tests - Used to test hypotheses when we are interested in a *specific* alternative to the null hypothesis - The research hypothesis is direction, posing either a mean decrease of a mean increase in the DV, but not both, as a result of the IV ex. Ho: μ=100 H1: μ > 100 2. the percent of variance that can be explained by a given variable. - Effect size tells us how much two populations *do not overlap* The ___ overlap the ___ the effect size - The ___ overlap the ___ the effect size 1. less overlap, larger effect size 2. greater overlap, smaller effect size Cohen's d - A measure of effect size in terms of the number of standard deviations that mean scores shifted above or below the population mean stated by the null hypothesis. The ___ the value of d, the ___ the effect in the population - larger d = larger effect smaller d = smaller effect Calculating effect size - Assesses difference between means using standard deviation instead of standard error d = (sample mean-population mean)/SEM Cohen's effect size conventions - d<.2 = small effect size .2<d<.8 = medium effect size d>.9 = large effect size Characteristics of Effect Size - Value being measured? *d* Type of distribution test is based on? *population distribution* What does it measure? *The size of a measured effect in the population* What can be inferred from the test? *The size of an effect from small to large* Statistical Power - Measure of the likelihood that we will detect an effect (i.e., reject the null hypothesis). • The probability that we will reject the null hypothesis (if it is indeed false); when we should reject the null hypothesis - *correctly rejecting the null hypothesis* - the probability of not making a Type-II error As effect size ___, power ___ - increases, increases - direct relationship As the size of an effect ___, the power to detect the effect ___. - increases, also increases - direct relationship Because a larger effect size is associated with greater power, it is easier to detect the larger effect. Factors that affect Power - 1. Effect size (increase d, increase power) 2. Sample size (increase n, increases power) 3. Alpha level (increase alpa, increase power) F 8-10 4. Turn a two-tailed hypothesis test into a one-tailed hypothesis (increasing power) Other ways to increase Power - • Exaggerate the mean difference between levels of the independent variable. • Decrease standard deviation Scatterplots - Graphs that depict the relationship between two ratio variables: one independent and one dependent Relationships observed - - linear = relationship between variables is best described by a straight line - nonlinear = relationship between variables is best describes by a line that breaks or curves How to create a scatterplot - 1. Organize data by participants; each participant will have 2 scores, one on each variable 2. Label x-axis with independent variable and its possible values 3. Label y-axis with dependent variable and its possible values 4. Make a mark on the graph above each study participant's score on the x-axis and next to his or her score on the y-axis 5. To convert to a range-frame, simply era the axes below the minimum score and above the maximum score