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Psych Statistics Midterm
Population - the set of all individuals of interest in a particular study Sample - a set of individuals selected from the population Parameter - a (usually numerical) value that describes a population. Usually derived from measurements of the individuals in the population. Statistic - a (usually numerical) value that describes the sample. Usually derived from measurements of the individuals in the sample Descriptive Stats - statistical procedures used to summarize, organize, and simplify data Inferential Stats - techniques that allow us to study samples and then make generalizations about the populations from which they are selected Sampling error - a naturally occurring discrepancy, or error, that exists between a sample statistic and the corresponding population parameter Correlational method - two different variables are observed to determine whether there is a relationship between them
What is the main difference between experimental and nonexperimental studies? - the way that the results can be explained. Experimental studies produce cause and effect explanations. Nonexperimental studies produce associated explanations What problems can arise in experiments? - Error can be introduced by: Participant variables-age, gender, intelligence, etc. Environmental Variables- lighting, time of day, weather, etc. Independent variable - the variable being manipulated by the researcher Dependent variable - the variable that is observed to assess the effect of the treatment Name 2 types of nonexperimental methods of study - Nonequivalent groups Pre-post studies pg. 16 Quasi-independent variable - the independent variable in a nonexperimental that is used to create different groups of scores Constructs - intangible variables that cannot be directly observed. ex: intelligence, hunger, etc. Operational definition - defines constructs and establishes a way of measuring them
consists of a set of categories that are organized in an ordered sequence. measurements of this scale rank observations in terms of size or magnitude Interval scale - consists of ordered categories that are all intervals of exactly the same size. equal differences are equal in magnitude. the zero point is arbitrary. ex: temperature Ratio scale - an interval sale with the additional feature of an absolute zero point. ratios of numbers reflect ratios of magnitude What is the difference between interval and ratio scale? - the arbitrariness of the zero. in the ratio scale, the zero is non-arbitrary and you can measure the distance from zero Notation: N vs. n - N= number of scores in a population n= number of scores in a sample Notation: X and Y - represent scores or variables Frequency distribution - a way of organizing scores based on frequency Frequency distributions: proportions and percentages - proportion= p= f/N percentage= p(100)= f/N (100) What is special about real limits in relation to frequency distributions? -
There are no gaps between intervals in grouped frequency distributions. for that reason, the interval widths are whole numbers How would you graph interval or ratio data? - With a histogram or polygon Polygon - looks like a line graph but for frequencies. scores are on the x-axis. frequency is on the y-axis What kind of graph is best for nominal or ordinal scale frequency data? - Bar graphs You can also use bar graphs for ___________. - relative frequencies. ex: females slightly higher than males in terms of frequency If a frequency distribution graph is drawn as a smooth curve, it is probably showing a _______________ distribution. - population distribution Percentile rank/percentile - the percentage of individuals in the distribution with scores at or below the particular value Cumulative frequency - That weird thing when you have a "cf" column and count the number of scores at AND below the score Cumulative percentage - The other weird thing when you do cf/N (100). The top value should start at 100% Weighted mean -
When there are extreme scores or skewed distributions; when there are undetermined scores in the sample; when you have an open ended distribution; ordinal scales When should mode be the go to for selecting a measure of central tendency? - When using data on a nominal scale; for discrete variables; for describing shape If a distribution is roughly symmetrical, what can we say about the mean and median? The mode? - the mean and median are close together in the center of the distribution. the mode is also near them if this is a unimodal distribution What can we say about the mean, median and mode in a symmetrical bimodal distribution? - the mean and median are close together near the center. the mode is located at the peaks of the distribution In a positively skewed distribution, state the relative locations of the mean, median and mode: - The mode is first at the peak, then moving from left to right, the median is next, then the mean In a negatively skewed distribution, state the relative locations of the mean median and mode: - The mean is close to the tail (left), next comes the median, then the mode is at the peak (right) Variability - measure of the differences between scores in a distribution and describes the degree to which the scores are spread out or clustered together For a continuous variable, the range is calculated by subtracting..... - The lower real limit of the lowest score from the upper real limit of the highest score Define: standard deviation - the average distance from the mean
Define: variance - the average squared distance from the mean. the mean of the squared deviations What is the relationship between standard deviation and variance? - the standard deviation is the square root of the variance Define: Sum of squares - the sum of the squared deviations What are the 2 formulas for SS? and which one are you responsible for? - There is the computational and the definitional. I am responsible for the definitional: SS= sum(X-mu)^ Notation: population standard deviation and variance - use lowercase sigma and lowercase sigma^ When would one want to use the computational formula for SS? - When the means or deviations are not whole numbers Notation: sample standard deviation and variance - use s and s^ WHEN FINDING SAMPLE VARIANCE AND STANDARD DEVATION, DONT FORGET TO USE ______________ IN THE DENOMINATOR OF THE EQUATIONS - n- Define: degrees of freedom - determines the number of scores in the sample that are independent and free to vary
An entire population of scores is transformed into z-scores. The transformation does not change the ___________ of the distribution but the ____________ is transformed into a value of 0 and the ____________________ is transformed to a value of 1 - shape mean standard deviation What is the sample z-score formula? - z= (X-M)/s Sample to population Population to sample What are these referring to? - inferential statistics probability Set probabilities in a normal distribution: - 34.13% for 0 to + 13.59% for +1 to 2 2.28% for 2+ In a binomial distribution, pn is....... - the mean, mu In a binomial distribution, sqrt(npr) is...... - the standard deviation, lowercase sigma In a binomial distribution, p+q equals.... - 1
USE REAL LIMITS FOR BINOMIAL DISTRIBUTIONS. Problem: What value would you use for X if you want the probability that 20 or more questions will be correct on true/false tests? - 19.5 (Lower real limit of 20) USE REAL LIMITS FOR BINOMIAL DISTRIBUTIONS. Problem: What value would you use for X if you want the probability that more than 20 questions will be correct on true/false tests? - 20.5 (Upper real limit of 20) What z-score represents the extreme 5% of a normal distribution? -
Define: distribution of sample means - the collection of sample means for all the possible random samples of a particular size (n) that can be obtained from a population Why do we study the distribution of sample means? - It gives us information that allows us to predict characteristics of a sample 3 Characteristics of the distribution of sample means -
- sample means pile up around population mean
- pile of sample means should form a normal distribution
- the larger the sample size, the closer the sample means should be to the population mean Central Limit Theorem - For any population with mean mu and standard deviation lowercase sigma, the distribution of sample means for sample size n will have a mean of mu and a standard deviation of l.sigma/squrt(n) and will approach a normal distribution as n approaches infinity The distribution of sample means is almost perfectly normal if..... -
Define: hypothesis test - a statistical method that uses sample data to evaluate a hypothesis about a population Define: alpha level/level of significance - the probability value that is used to define the concept of "very likely" in a hypothesis test Define: critical region: - the area of extreme sample values that are very unlikely (as defined by the alpha level) to be obtained if the null hypothesis is true. If sample data fall in the critical region, the null hypothesis is rejected. Type 1 error - when a researcher rejects a null hypothesis that is actually true. Simply, you conclude that the treatment has an effect when it really doesn't. Define: alpha level - the probability that a test will lead to Type 1 error in a hypothesis test. Simply, the probability of obtaining sample data in the critical region even though the null is true Type 2 error - when a researcher fails to reject a null hypothesis that is really false. Simply, the hypothesis test has failed to detect a real treatment effect When you reject the null hypothesis in a hypothesis test, you can conclude that.... - the result is statistically significant Factors that influence a hypothesis test -
- variability of the scores
- The number of scores in the sample
A research report summarizes the results of the hypothesis test by stating, "z= 2.13, p< .05". What would be a correct interpretation of this report? - The null hypothesis was rejected and the probability of Type 1 error is less than. A two-tailed hypothesis.... - does not specify the direction of the hypothesis for the population mean A one-tailed hypothesis... - specifies either an increase or decrease in the population mean. Simply, this test makes a statement about the direction of the effect Define: effect size - a measurement of the absolute magnitude of a treatment effect, independent of the sample size. How do you measure effect size for a hypothesis test? - use Cohen's d Formula for Cohen's d - (M of treatment - mu of no treatment)/ sigma Magnitudes of d - d=.02 is a small effect size d=.5 is a medium effect size d=.8 is a large effect size Define: power - the probability that the test will correctly reject a false null hypothesis. Simply, the probability that the test will identify a treatment effect if there really is one.
What table is used for t distributions? What table is used for z-scores? - t distribution table unit normal table What factors influence estimated standard error? - variance- proportionally sample size-inversely If a t statistic is computed for a sample of n=4 scores with SS=300, then what are the sample variance and the estimated standard error for the sample? - s^2= 100 s sub m= 5 What are the 2 methods of measuring effect size? - Cohen's d r^ t statistic: Cohen's d What does it mean? - still measures the effect size. (M-mu)/s. The size of the treatment effect is equal to blank t statistic: r^2 - The percentage of variance accounted for by the treatment (t^2)/ (t^2 + df) r^2 effects: - .01 is small effect .09 is medium effect
.25 is large effect t statistic: confidence interval - mu= M +/- t(s sub m). an interval of values centered around a sample statistic How to report the results of a t-test - The infants spent an average of M=13 out of 20 seconds looking at the attractive face with SD=3.00. Statistical analysis indicates that the time spent looking at the attractive face was significantly greater than would be expected if there were no preference, t(8)=3.00, p<.05, r^2=. Note: Directional t tests are a thing - Independent measures/ between subjects design - a research design that uses a separate group of participants for each treatment condition (or for each population). AKA two separate samples used to obtain two groups of scores to represent two populations or two treatment conditions being compared Repeated measures/ within subjects design - two sets of data are obtained from the same group of participants For Independent measures design you basically do.... - everything like a normal t-test except that you extend the equations by adding or subtracting the 2 sample data Independent measures null hypothesis: - Ho= mu1 - mu2= 0 How to report a directional one tailed test: -
Null hypothesis for a one tailed repeated-measures study - Ho= mu sub d> or equal to 0 Advantages of repeated-measures design compared to independent measures design -
- uses fewer subjects
- studies change over time
- reduces problems caused by individual differences Disadvantages of repeated measure design -
- Time related factors
- order effects Factor - The independent variable of an ANOVA Hypothesis for ANOVA - Ho= mu1=mu2=mu SStotal - fancy equation using grand total SS within treatments - sum (SS inside each treatment) SSbetween - SStotal- SSwithin df total - N-
df within - N-k df between - k- F - MSbetween/MSwithin Post Hoc Tests - additional hypothesis tests that are done after an ANOVA to determine exactly which mean differences are significant and which are not Tukey's HSD Test - commonly used. computes a single value that determines the minimum difference between treatment means that is necessary for significance Scheffe Test - extremely cautious method used for reducing the probability of type 1 error Relationship between ANOVA and t tests - F= t^ Effect size for repeated measures ANOVA - eta^2= SSbetwtreatments/(SSbetwtreatments + SSerror)
