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An overview of descriptive and inferential statistics, including measures of central tendency and dispersion, sampling error, z-scores, and hypothesis testing. Topics covered include the difference between experimental and nonexperimental studies, real limits, interval and ratio scales, frequency distributions, and the central limit theorem.

Typology: Exams

2023/2024

1 / 20

Download Statistics: Descriptive & Inferential Methods, Sampling Error, Z-Scores, Hypothesis Testin and more Exams Psychology in PDF only on Docsity! 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 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 - calculating the mean when combining multiple sets of scores. Multiply (M)(n) for each sample to get sums then for each set. Then add the set sums and divide by the total n from both sets Key thing to remember when calculating mean from a frequency table: - Make sure to extract all scores from the table to get the sum What happens to the mean if you replace one score with a higher number? - the mean will increase What happens to the mean if you remove a score that is equal to the mean? - nothing What information do you need to be able to calculate a new mean if you add or subtract a score from the original set? - M, sum of X, and n for both the new and old samples. you can calculate info for the new sample using the old What happens to the mean if you add or subtract a constant from every score in a sample? - the same constant will be added or subtracted from the mean What happens to the mean if you multiply or divide a constant from every score in a sample? - the same constant will be multiplied or divided by the mean When the number of scores in a set is odd, the median is...... - the middle number When the number of scores in a set is even, the median is..... - the average of the two middle numbers When should median be the go to for selecting a measure of central tendency? - 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 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 +1 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? - 1.96 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 - 1. sample means pile up around population mean 2. pile of sample means should form a normal distribution 3. 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..... - 1. The population that the samples came from is a normal distribution 2. the number of scores (n) is large, around 30+ The "expected value of M" in a distribution of sample means should..... - be equal to the mean of the population of scores, mu What is the purpose of the standard error of M? - 1. To describe the distribution of sample mean by showing how much difference is expected from one sample to another 2. It measures how well an individual sample mean represents the entire distribution. Basically, how much distance is reasonable to expect between a sample mean and the overall mean for the distribution of sample means Define: Standard error of M - The standard dev. of the distribution of sample means (sigma sub m). It provides a measure of how much distance is expected on average between a sample mean (M) and the population mean (mu) Law of large numbers - the larger the sample size (n), the more probable it is that the sample mean will be close to the population mean When n=1, the standard error equals.... - the standard deviation Formula: standard error of the mean, sigma sub m - l.sigma/squrt(n) What happens to standard error when you increase sample size? - the error gets smaller Factors that increase power - - increase sample size Factors that decrease power - -increase value of l.sigma When do we use z-scores? - When the population standard deviation (or variance) is known so that we can compute the standard error When the population standard deviation is unknown, what do we do? - we find the t statistic Define: estimated standard error (s sum m) - an estimate of the real standard error (sigma sub m) when the value of l.sigma is unknown. used in t statistics You must use ______________ for t statistics because it is utilizing sample information - degrees of freedom!!! In t statistics: What does a larger sample size do to the t distribution? - it makes it taller and less spread out In t statistics: Describe a t distribution of df=20 relative to a distribution of df=5 - the df=20 distribution will be taller and less spread out because the sample size is larger How does the shape of the t distribution compare to a normal distribution? - the t distribution is flatter and more spread out, especially when n is small 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^2 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=.5294 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: -