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by: Mary Kay

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PSYC 2300 Study Guide 1 PSYC2300

Mary Kay
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PSYC 2300 Introduction to Statistics Midterm Exam 1 Study Guide
COURSE
Introduction to Statistics
PROF.
Hipp, Daniel
TYPE
Study Guide
PAGES
8
WORDS
CONCEPTS
Psychology
KARMA
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This 8 page Study Guide was uploaded by Mary Kay on Saturday October 1, 2016. The Study Guide belongs to PSYC2300 at University of Denver taught by Hipp, Daniel in Fall 2016. Since its upload, it has received 22 views. For similar materials see Introduction to Statistics in Psychology (PSYC) at University of Denver.

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Date Created: 10/01/16
Study guide 1 Decision Making • The probability of it’s occurrence must be < .05 (i.e., 5 in 100, or a 5% chance). • Chance differences between the means is called “Sampling error" • If the probability of obtaining a particular sample mean by chance is .05 or lower,  statisticians/ researchers conclude that it is too unlikely to be due to chance along.  ◦ This is also called an “Aloha Level” (a)=0.05 • One • two Tails, Z=1.96,   0.025 • One tails, Z=1.65,   0.05 • If the difference is not due to chance, then, you infer that the difference is due to the IV. Formalities of Significance testing Statistical Hypotheses: Statements that describe the hypothesis that we are trying to test  in statistical language.  • Null Hypothesis ◦ No real difference between the population mean that is represented by our sample mean  and the population mean to which we are comparing it.  • Alternative Hypothesis: States that there is a difference between the population mean that is represented by our ample statistic and the population parameter.  ◦ If Ha is true, the IV did work (IV did affect DV) One­tailed vs. Two­tailed • If you hypothesize that the dependent variable will be affected in a specified direction ,  the one­tail test.  ◦ e.g. Ginseng will increase intelligence.  ◦ H0: U IQ after herb <=100 ◦ Ha: U IQ after herb >100 • eg,. zobt=1.6 is below the critical value of 1.65. therefore, we retain the null hypothesis.  There is no evidence to suggest that taking the herb will increase IQ scores. The 4 point  difference between the sample mean and the population mean was not statistically  significant.  • To retain the null hypothesis: ◦ The null hypothesis is assumed to be true, but you cannot prove the null hypothesis.  • Even is there is no statistical difference between the groups, there may still be a  difference in the underlying populations. But we are not able to detect it with our  statistical procedures.  Two­tailed Conclusion • eg,. zobt=2.67 is higher the critical value of 1.65. therefore, we retain the null hypothesis. There is no evidence to suggest that taking the herb will increase IQ scores. The 4 point  difference between the sample mean and the population mean was not statistically  significant.  • Reject the null hypothesis ◦ It is very unlikely that the difference between your groups is due to chance.  Assumptions of the z­test • The dependent variable is interval or ratio. • You know bother the mean and the standard deviation of the population. (Hardly  happnened) Two possible types of errors: • Type 1 error Alpha ◦ No effect of IV ◦ Occurs when the null hypothesis is true, but we (Wrongly) reject the null hypothesis.  (Like an innocent person being convicted) ◦ Alpha: The probability of making a type 1 error is qual to the probability of getting a  sample mean by chance.  ◦ If we use alpha> 0.05, the probability of making a type 1 error is always less than 0.05.  • Type 2 error: Beta ◦ Falsely retaining the null hypothesis.  ◦ IV has an effect ◦ Retain H0 (No difference), e.g..in middle • 1­alpha ◦ No IV effect,  ◦ H0 reject the null hypothesis.  • 1­Beta ◦ IV has an effect Power is determined by • Alpha: increasing your alpha • N: the larger you sample size, the more power • Effects size: different between the means , relative to the variable size.  Hypothesis testing • Z­test: When you know mean and stander deviation  • Single (one)sample T­test: when you know U but do not know stander deviation  Central Tendency  Average value: mean value • Most Frequent score • Mathematical average of all scores • Middle position • Sample mean= sum of X / N • Sample mean  = xx • Population mean =  μ The mode • The score that occurs most frequently in a sample.  • Find it by construct a frequency distribution. • use it when you have nominal data • isn’t so great ◦ Ignores all data except the most frequently occurring score. ◦ Can have bimodal or multimodal data The Median • The score at the 50th percentile: • exactly have of the scores are lower than the median and exactly half of the scores are  higher.  Percentile: the point in the distribution below with __th percent of the scores fall, e.g. the  25th Which measure of Central Tendency should you use? Use the mean unless • you have nominal data, use the mode. e.g., to find the “Average “ major, average eye  color... ◦ The modal response was to do better in school; 20% of all students reported that this was  their resolution.  • If you have a skewed distribution, use the median.  • use the median for ordinal data.  Normal distribution. 3 equal Median larger in Negatively skewed, on the right Different ways to measure variability in your data set. • Range... • Find Sample mean • Deviation from the mean. 1 The size of the deviation indicates how far a particular score is from the  mean. 2 The higher the score, the more deviation from the mean.  3 In a normal distribution, the greater the deviation, the less frequent the  score.  variance: (S^2) the average of the squared deviations around the mean. • ((x­xx)^2)/N   Standard Deviation: (S)    The square root of the average squared deviation around the   mean .  • Stander deviation sd is the average amount that the scores in your sample deviate from he mean.  • It will always be a positive number.  • Larger number, larger variable in the data.  Unbiased Estimator (a hat above S) • variance: ((x­xx)^2)/(N­1) • Because samples tend to have less variability than the parent population Z scores and Z distributions • You can transform a score into a z­score to conveys information about relative position  and relative frequency of that raw score.  • “Standardized” the score by taking into account a mean and a standard deviation ◦ Makes scores from different distributions comparable • Most useful with a normal distribution.  why standardize your scores? • to have information about position in a distribution. • To compare • z=(x­xx)/Standard Deviation  • z higher, did better on the exam.  • It is Measured in terms of the number of standard deviations from the mean. • Generally range from ­3.0 to 3.0 ◦ Why? 99.7% of scores fall with in this range. • A z­score of 0 means that the score is at the mean. • A negative Z score means that a score is below the mean • e.g. Z=1.0: Raw score is 1 standard deviation above the mean.  • e.g. Z=­0.5: Raw score is 1/2 standard deviation below the mean. Convert Z back to raw score. • Sample X=z*stander deviation +  xx Inferential stats: • Significance testing or hypothesis testing • Z­test • t­tests (Different types) • ANOVA (different types) • Chi­square How most experiments works Simple Probability • Number between 0 and 1 (a proportion) • Probability of event A is written as “P(A)" • If P(A)= 0.1 it indicates with certainty that event A will happened.  Two types of probability Distributions • Empirical probability distribution ◦ Based on an actual frequency distribution/frequency data • Theoretical probability distribution: • Based on a theoretical normal distribution • Eg. your z­table Standard error of the mean  Different types of Statistics • Descriptive vs. Inferential • Frequency vs. Proportion Statistics Data is plural. Datum is the singular form Populations and Samples • Population: The entire set of individuals that you want to know about. Just number  change, no any condition change.  • Sample: The relatively small subset of scores or individuals that you have available to  observe.  What is a good sample? • One that allow you to generalize beyond your sample to a population. ◦ Randomly selected from the population of interest.  1 If truly random: each person in the population has an equal  probability of being selected.  ◦ Representative of the population 1 Characteristics of sample mirror those of the population of interest. Two types of statistics • Descriptive: Organizing, summarizing, and looking for relationships in a sample or a  population.  ◦ Average G.P.A ◦ Most typical college major • Inferential: techniques that tell us whether the strength of the relations in our data allow is to generalize beyond our sample to the population Variables: A variable is anything that can take on more than one value.  Relation: When a change in one variable systematically leads to a change in another  variable.  • Height and weight • Diet and disease • Alcohol and aggression Two ways to study relations between variables: • Correlational Study ◦ Measure two things and determine whether there is a relation between them.  ◦ In correlational studies, nothing is manipulated by the researcher.  ◦ Correlation does not equal causation. 1 Third variable problem: there may be some other variable • Experiment Study ◦ Researcher manipulates a variable and measures the effect on another variable, while  holding everything else constant.  ◦ Researcher randomly assigns subjects to groups ◦ If everything else is controlled, you can (Tentatively) infer a causal relationship.  Types of Variables in Experiments: • Dependent Variable  1 The behavior that is measured by the experimenter.  1 Exam score 2 Reaction Time • Independent Variable  1 The variable that is manipulated by the experimenter to see if it affects the  behavior of interest.  1 Hours of sleep 2 Alcohol Consumption 2 Called factors.  • E.g.: iv hours of sleep: condition levels are 4hrs, 6hrs, 8hrs. • Quasi ­ independent variables 1 Gender 2 Age 3 Race 4 Religion • Many of the same questions can be addressed by both correlational studies and  experiments, but stronger conclusions can typically be drawn from the experiment.  Classification some variables.  • IV vs. DV • Quantitative：specifics an amount 1 Age, gpa • Qualitative: Specifies a category.  1 Gender, color Types of data Nominal Data • Nominal = name ◦ Differ only in kind (Different categories) 1 e.g. Gender, religion, Major ◦ Can’t order the values.  1 Assigning numbers doesn’t mean an amount of something ◦ Qualitative Ordinal Data • Ordinal = order • Ranking, preferences ◦ e.g. sports standings, class rank, Olympic medals • Can't make assumption about the degree of difference. Interval Scale • Ordered categories of the same size.  • Equal space between interval • No “Real” 0 as origin of the scale (Can’t have “no temp”). 1 On a scale of 1­7... Ratio Scale • Intervals are equally space • Has a “Real” 0 • Quantitative 1 e.g., height, weight, unit of time, 10, 20, 30, GPA, books you read. The type of statistical procedures that you can do depend on the variables that you study.  Frequency ­ f • Describing A single variable • N ­ total set • Relative Frequency = f/N is between 0­1 • cf = cumulative frequency: the sum of all the frequencies of all scores at or below a  particular score.  • rel cf = relative cumulative frequency. (There are must have a 1) • Average = mean score Normal Distributions is, by far, the most frequently occurring type of distribution.  • Most human characteristics are normally distributed ◦ Height ◦ Intelligence ◦ Athletic Ability Positively Skewed • A few extremely high scores are raising the tail not the right. It is not balanced with  corresponding low scores.  • Company salaries. • High peak in left Negatively Skewed • High peak in right.  Bimodal Distribution • Two high frequency points.

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