Psych 71
Hypothesis test
a statistical method that uses sample data to evaluate a hypothesis about a population Based on the probability of observing some sample statistic if a certain hypothesis is assumed to be true
A researcher wants to know whether a presentation on the health benefits of Brussels sprouts would change people's attitude towards Brussels sprouts. She recruited 84 undergraduates. Before the intervention, she asked participants to rate their attitude towards Brussels sprouts. After the presentation, they rated their attitudes again. Which t-test is appropriate?
answer: Dependent samples explanation: There is one sample of individuals, everybody is being measured the same, and given the same presentation.
A: Does a strong correlation imply that the regression coefficient will be large? B: Does a large regression coefficient imply that the correlation will be strong? [answer for A / answer for B]
answer: No/No explanation: A strong correlation implies that the points form a tight line, but does not say anything about the correlation. There can be strong correlations and low slope. A big slop does not tell anything about the correlation.
Kaiqi is interested in how studying for the GRE in a foreign language can be improved. She manipulates whether participants study new vocabulary by seeing definitions or contextual sentences, as well as whether those definitions/sentences are presented in the native language (Chinese) or the language of the test (English). All participants study 5 new GRE words in each of the 4 conditions and are tested on all 20 words using real GRE test items. Which type of analysis is appropriate for this design?
answer: factorial repeated measures analysis explanation: there is repeated measures and test ecah possibility
Why do we try to falsify the null hypothesis rather than support the alternative hypthesis
answer: we know what the population parameters would be under the null, but we don't know precisely what they would be under the alternative\ Explanation: We are hypothesizing a mean correlation of zero, so we do know some of the parameters. The null hypothesis gives a specific parameters of the distribution
Assume that, on average, healthy young adults dream 90 minutes each night, as inferred from a number of measures, including rapid eye movement (REM) sleep. An investigator wishes to determine whether drinking coffee just before going to sleep affects the amount of dream time. After drinking a standard amount of coffee, dream time is monitored for each of 28 healthy young adults in a random sample. Results show a sample mean of 88 minutes and a sample standard deviation of 9 minutes. Which analysis is appropriate for testing the investigator's hypothesis?
answer; one- sample t-test
If the counselor wishes to determine whether scores on an anxiety test change for the same group of clients at before and after a consultation, what would be the appropriate test?
dependent samples t-test
If the researcher wanted to compare the difference in stress levels between husbands and wives in heterosexual marriages, what would be the appropriate statistical test?
dependent samples t-test
To determine whether speed reading influences reading comprehension, a researcher obtains two reading comprehension scores for each student in a group of high school students, once before and once after training in speed reading.
dependent-samples t-test
If a design has no main effects, there should be no interaction.
false
General Linear Model
grand mean- treatment offset- residual-
Alternative hypothesis (h1)
In the population there is a change, a difference, or a relationship For an experiment, this means an effect of treatment The difference observed is due to sampling error AND a real effect Treatment =/ u without treatment
Statistical hypothesis: Null hypothesis
In the population there is no change, no difference, or no relationship. ( for an experiment, this means no effect of treatment The difference observed is due to sampling error only U treatment = uwithout treatment
Logic of Chi-Square (test of independence)
- does not expend on population parameters Null hypothesis: the predictor and the outcome are independent (there is no relationship between the variables) Alternative hypothesis: the predictor and the outcome are dependent (there is a relationship between the variables) Expected frequencies: tells us what the cell counts should be if the null hypothesis is true (i.e if there is no relationship in the population) The chi square test static quantifies how closely the observed frequencies (from our sample data) and expected frequencies "match" If they are "close enough", the test statistic is small and we retain the null If they are 'different enough", the test statistic is large and we reject the null hypothesis
General form of the T statistic
-A t statistic (no matter which type) have the same general form: the sampling error(i.e the difference observed sample statistic and the population parameter ) divided by the standard error of that statistic (i.e the standard deviation of the sampling distribution of sample statistics) t= sample statistic -population parameter/ estimated standard error of statistic
We know that IQ is a variable that is normally distributed in the population, with a mean of 100 and a standard deviation of 15. Use the empirical rule to estimate what proportion of individuals in the population we would expect to have an IQ higher than 130.
2.5 explanation: you would see the tail end percent, in order to find the answer
One-sample T-tests
A one-sample t statistic for is the difference between the sample mean and the population mean (i.e the sampling error) divided by standard error of the mean (i.e the standard deviation of a sampling distribution of sample means t= sample mean- population mean/ estimated standard error of mean Similar to a z- score, this tell us how extreme our observed sample mean is relative to all possible sample means we could have observed if the null hypothesis were true
z-test vs. t-test
A one-sample t-test is very much like a z-test The only difference is whether the population standard deviation (sigma) is known (z-test) or must be estimated from the sample data (t-test) Requires knowledge of u and knowledge of o While the other requires the knowledge of u and requires the estimation of o
P - value (proportion more extreme value
A p-value is a way of describing how extreme a score is in a distribution. A p-value is the proportion of a distribution more extreme than a given score What proportion of possible sample statistics are larger than the statistic from our sample If the null hypothesis is true, how likely are we to observe this statistic by chance alone? A two tailed is more conservative and will be twice as big as the one tailed test
What is the difference between a predicted score and a group mean?
A predicted score is the same thing as a group mean
The general linear model
A system of equations that is used as the mathematical framework for most the statistical analyses used in applied social research A model in a way of representing patterns in data data= model +error Models can be simple or complex The mean of a distribution is one (very simple) model of the data Models can have many additional terms to represent different "effects" of interest (main effects, interactions, covariates, etc.) The general linear model (GLM) is "linear" in the sense that it is written like an equation for a line (y=mx+b) Also implies that each data point is a linear sum of all the components of the equation grand mean-
Type 1 vs. Type 2 error
A type 1 error is when there is no effect is present but a researchers rejects the null hyposthesis " false alarms" or "alpha error" A type 2 error is when a real effect is present but a researcher fails to reject the null hypothesis " miss" or "beta error" When we fail to reject the null when it is true its called correct retention When you reject the null hypothesis and it is true then this is a type 1 error (false alarm) Is h1 is true, but it is not rejected , that is the type 2 error When h1 is true and you reject is the correct rejection
The normal distribution:
According to the central limit theorem, the SDoM will be normal as long as the sample size is large... and we know some pretty useful things about normal distributions All normal distributions share this function, but they differ according to 2 parameters : mu and sigma The empirical rule: the central limit theorem guarantees all sample means are essentially drawn from NORMAL DISTRIBUTION of possible sample means The means we can assess the probability of observing a range of sample means by relying on known probabilities in the normal distribution
Manipulating multiple factors
Allows us to answer questions about whether the effect of one independent variable depends on the level of another Factorial design; each level of one IV is combined with each level of the others to produce all possible combinations of levels Also sometimes called a "crossed" design because the levels of one factor are crossed with the levels of another
How unlikely is Unlikely enough to reject Ho
Alpha = the probability value that we use to determine which sample outcomes are considered very unlikely if the null hypothesis is true ( this probability level is chosen by the researcher! (does not have to be 0.05) Critical region= the region of the sampling distribution that contains the sample outcomes that are considered to be very unlikely if the null hypothesis is true. - this area depends on: what alpha is whether the test is one or two tailed - critical value= the value(s) that define the boundary of the critical region(s) (these values depend on ; what alpha is and whether the test is one or two tailed
Which of the following statements about alpha and p is TRUE?
Alpha and P are both areas under the curve of the sampling distribution explanation: A and D are false because Alpha is not calculated and always chosen and p is the test statistic. C is wrong because alpha and P will always be in the tails.
what is the relationship between alpha and the critical region
Alpha is the size of the critical region explanation: An alpha and critical region are areas. critical region is the grey area and the alpha tells us how big that area is is. The boundary is the critical value.
In a chi-square test of independence, what do the "expected" values represent?
Answer : the expected count in each cell if the two factors vary independently explanation: the first (the expected count in each cell if all cells have equal counts)and the second options (the expected count in each cell if the two factors vary independently) are wrong for the same reason, unless the independent effect is that they are equal. no relationship does not mean equal. C and D (the expected count in each cell if there is a relationship between the factors) are opposite in nature, and there is no relationship.
If we run a hypothesis test with an alpha level of 0.05, what is the probability that we would make a type II error if the null hypothesis is true?
Answer: 0% explanation: Because there is nothing to missed, the probability is 0. Answer would be A (5%)if asked about a "type 1) error. It would b (95%)if it was correct retention.
Robert is interested in the effects of age and emotion on memory. He conducts a study in which he manipulates participants' emotion: participants complete a memory task once after being induced to feel happy and once after being induced to feel sad. Participants are either children (ages 8-15) or young adults (ages 18-25). He measures each subject's memory using a recognition test paradigm. What kind of design has Robert used?
Answer: 2x2 mixed design factorial explanation: It cannot be within-subjects design because it is using different groups. Age has to be between, because you cannot be a different age at the same time. This is a mixed design because we have one within and between factors.
What is the difference between a treatment offset and a group mean?
Answer: A treatment offset is what you add o the grand mean to get the group mean
If the null hypothesis in a one-way ANOVA is that all of the treatment offsets are equal (and equal to zero), what could we say about the groups if we reject the null hypothesis?
Answer: At least one of the groups has a different mean from the others Explanation: Any of these could be true, but C is certain because it is the very least (min) that could be true
A drug and alcohol researcher is interested in studying the effects of alcohol on learning ability of college seniors. She randomly assigns 10 students to an "alcohol group" and another 10 students to a control group. The students in the alcohol group all receive 8 oz of alcohol prior to being tested. Then all of the students are run through a learning assessment and the number of errors is recorded and compared between conditions. Which t-test is appropriate?
Answer: Independent samples explanation: You cannot compute scores if there is no other measures to compare to, so it has to be independent samples
A school psychologist wishes to determine whether reading comprehension scores are associated with the number of months of formal education, as reported on school transcripts, for a group of 12-year-old children of migrant farm workers.
correlation
A group of researchers is interested in how stereotype threat affects performance on an intelligence test and whether positive affirmations can reduce the effect of threat. In their study they have 3 conditions: no threat + no affirmation, threat + no affirmation, and threat + affirmation. What is the appropriate notation to describe their design?
Answer: None of the above Explanation: None of these work because it is not a factorial design. It is a one way ANOVA. It is missing one of the conditions within the design. You will never see a 1, because it is not really a factor.
A researcher wants to know whether blood oxygen levels before a workout is related to lactic acid (soreness) after a workout. The researcher recruited 64 young adults and measured their blood oxygen levels before their workouts and lactic acid buildup after their workouts. Which t-test is appropriate?
Answer: none of the above explanation: it is none of the above, the difference score is meaningless because they are not comparing groups. If they are comparing variables , then you can use correlation
Between vs. Within-subject Factorial design
Between subjects factorial design All of the factors are manipulated between subjects Each subject participates in just ONE condition Within- subjects factorial design All of the factors are manipulated within subjects Each subject participates in ALL conditions Mixed design factorial Some of the factors are manipulated between subjects, SOME within subjects Each subject participates in MORE THAN ONE, but NOT ALL conditions
How can we do this without actually taking 100,000 samples and counting how many meet our criterion?
By relying on the mathematical properties of the normal distribution
A political scientist wishes to determine whether males and females differ with respect to their attitudes toward the funding of energy conservation programs by the federal government. Respondents indicate whether they support or do not support such programs.
CHI- SQUARE TEST OF ASSOCIATION
Repeated measures designs increase our power to detect a significant effect of condition because including person as a factor in the model...
Decreases the mean square error explanation: We are taking some of the mean square out. We are not changing the treatment means. Because we can account for each person, it would decrease the error. it shrinks the variance on the residuals.
An educational psychologist wants to check the claim that regular physical exercise improves academic achievement. To control for academic aptitude, pairs of college students with similar GPAs are randomly assigned to either a treatment group that attends daily exercise classes or a control group. At the end of the experiment, GPAs are reported for the seven pairs of participants. Which analysis is appropriate to test the difference between these two groups?
Dependent samples t-test
Effect size and Confidence intervals
Effect size- common statistical procedures involve null hypothesis significance testing (NHST):if p-value is below some threshold, we reject H0, if it isnt, we dont!... but how do we determine how big an effect is ? Effect size: numerical description of the strength of the relationship between variable (or the size of the difference between groups) There are many ways to express this Cohe's d; if it produced by random chance , used to visualize in the distribution r(squared)
Karisa is interested in the effect of study music on memory. In her study, all participants studied a list of words and later took a recognition test. Karisa manipulated the kind of music participants listened to while they studied: either rap or metal, and either with or without lyrics. Each participant heard only one type of music. Which type of analysis is appropriate for this design?
Factorial ANOVA (between subjects) explanation: There are two independent variable and "either or" = between subjects. There are no repeated measures in this design
Test Statistics
How do we know if our sample mean is unlikely enough to reject HO A test statistic tells us whether our sample is high. Low, or average relative to all the possible sample we could have observed under the null distribution Bigger numbers (+ or -) are more "extreme" More- extreme values are less likely
If you were to randomly draw scores from a population with µ=100 and σ=15, would you be more likely to observe a single score lower than 85 or a sample mean lower than 85? Explain your reasoning.
I would be more likely to observe a single score lower than 85 because it is an extreme value. That sample mean, would always be narrower that the sample population. As the sample size, increases the less likely it would have a sample mean lower than 85.
The logic of hypothesis testing
If collecting data from a sample, how can I make an inference about the population it was drawn from? Especially considering that I know different random samples will have different estimates of the population parameters?
Establishing a standard of evidence
If the goal is to falsify Ho then what counts as evidence against Ho? If Ho is true, then some sample means are more likely than others
An investigator wishes to determine whether, on average, cigarette consumption is reduced for smokers who chew caffeine gum. Smokers in attendance at an antismoking workshop are randomly assigned to two groups—one that chews caffeine gum and one that does not—and their daily cigarette consumption is monitored for six months after the workshop. Which analysis is appropriate to test the difference in cigarette consumption between the groups?
Independent samples t-test or one-way ANOVA
The logic of ANOVA
Is a way of capturing how much"overlap" there is among the sampling distributions for the different groups by comparing variations between groups to the variation within groups When variation between groups is low and within groups is high, then it is hard to tell whether the groups are really different or not When variation between groups is high and within groups is low, them it is easy to tell that the groups are different When we are asking between groups we are talking about the distance.
What is Anova ?
It is used to analyze difference between 3+ groups at the same time The analysis focuses on the variances of the components of the general linear model " analysis" often means "breaking apart" which exactly what we'll do: We've already seen how to decompose into component parts (the grand mean, the treatment offset, and the residual ANOVA will compare the variance of the treatment offsets to the variance of the residuals
The counselor is interested in whether there's a tendency for short courtships (i.e., duration of relationships prior to marriage) to result in early marital difficulties. If the counselor wants to test the relationship between years of courtship and years of marriage for clients, what would be the appropriate statistical test? Correct!
correlation
Kinds of statistical Effects
Main effect On average, are the levels of one factor different from each other? One way design (are the scores on the dependent variable different) Simple effect At a specific level of one factor, are the levels of the other factor different from each other? (narrowing in on one level on one factor) Interaction Is the pattern/effect at one level of a factor different from the pattern/ effect at another level of that factor. (difference in simple effects) (the effect of one factor depends on the levels of the other factor(s); difference between simple effects Parallel lines indicate NO interaction -> the effect of quality does not depend on price= the effect of quality is the same for cheap and expensive There is a problem with ANOVA if it is not independent
Imagine that some bimodal distribution has a mean of 12 and a standard deviation of 3. If I z-score that entire distribution, then what will the resulting z-scored distribution look like?
Mean=0, SD=1, shape= bimodal explanation: if the sample size was more than 30, the answer would be D. The mean would be 0 and our shape would be unchanged because you do not change the shape of the distributions by changing the numbers.
Cohen's D
Measure of effect size for difference between two means. Expresses difference between means in standard deviation units mean 1 - mean 2/ standard deviation(pooled) , in other words, how many standard deviations are the two means?
Meta -analysis and estimation
Meta-analysis: quantitative analysis of the results of many similar studies to find overall effect size Forest plot-> How much: effect size of each study How wrong: confidence intervals What else is known: Illustrates variations across studies
Pearson's R
Numerator= the sum of cross products - where we are multiplying deviation on x and the deviation on y denominator= sum of squares x and y Posit correlation- stronger correlation No relationship= more evenly distributed
Z scores : describing locations of scores
Often, we want to be able to tell whether a score (or a sample mean) is high, low,or average for the variable we are measuring If a student scored 79 on the quiz, was his score high, low, or average We can't tell without knowing more information What if I tell you the mean was 77? What if I tell you the standard deviation was 0.9 A raw score, by itself, doesn't tell us much, but we can transform that score into something more meaningful Z-scores : a representation of a score's deviation from a mean in terms of standard deviations Sign (+ or -) indicates whether the score is above or below the mean Value indicates the number of standard deviations the score is the mean left( greek letters population) right (sample) A linear transformation preserves the relative position of the scores, while changing the center and the scale of the distribution
In a correlation test, a negative r means...
On average, Y decreases when X increases answer: negative means that they move in opposite direction and it is an average
A researcher conducts an experiment investigating what types of activities cause boredom. She randomly assigns subjects to either read a dictionary for one hour or do a series of simple math problems for one hour. (Each subject does only one task.) The subject is then asked a simple yes/no question: "Would you rather have done nothing at all for an hour than do the task you just completed?" The researcher predicts more people will answer "yes" after doing math problems than after reading the dictionary. Which statistical test must the researcher use to test her hypothesis? Explain how you know.
Our predictor variable is activity and its operationally defined as the dictionary vs. math. This variable is categorical. The DV is boredom and it is operationalized as a yes/no question. This variable is categorical. The appropriate test would be a chi- square test of independence.
Calculating A P-value
P-value still refers to the proportion of samples with a test statistic this extreme or more extreme Probability is drawn from a chi-square distribution Shape of distribution is affected by degrees of freedom df= (r-1)(c-1)
Degrees of Freedom
Pieced of independent information that go into a calculation Thought experiment : create several samples of 5 observations, each with a mean of 10- how do you choose the values? How many values can be chosen at random to ensure you get a mean of 10 Why use degrees of freedom(n-1) instead of sample size(n)? When n deviations from the sample mean are used to estimate variability in the population, only n-1 are free to vary (because of restriction that the sum of all deviations must equal zero) therefore , only n-1 sample deviations supply valid information for estimating variability Not doing this adjustment would cause us to underestimate variability in the population
Decision errors
Possible truths and possible decisions Only one of these can be true )they are mutually exclusive) We make only one of these decisions based on sample data
Confidence interval
Range that is likely to contain the true population value - therefore, 95% confidence interva = 95% confidence that interval contains true value (eg. study observes 5 pt difference between two groups , 95% CI might be 3pt to 7 pt Gives clearer picture of precision with which study has estimated population value Results of familiar statistical test can be expressed through confidence intervals If 95% CI does not include null value, the the test is significant
Simple Linear regression Model
Regression models - x variables are interval or ratio scaled Mean structure Models (analysis of variance Models) X Variables are Nominal or ordinal scaled Simple Linear Regression: a procedure for finding the best fitting *straight*line for a set of data using a simple predictor variable-> the result is called the linear regression line.-> basically finding the best slope intercept for our model b1= is the slope, what is the expected change Predicted value= on the line y= individual score
Which of the following sampling distributions of sample means would we expect to have a normal shape?
Sample of size 20 drawn from a normal population & samples of size 50 drawn from a skewed population explanation: A and C are correct, because normal distribution would always be normal and high sample size would create normal shape.
Estimation thinking
Science is cumulative: the result anyone study can ve tenuos, but the cumulative evidence from a body of research can be compelling Three questions to ask: "How much?" (i.e the effect size) " How wrong?" (i.e., sampling variation) "What else is Known?" (i.e., synthesizing multiple results
drawing conclusions ad parameters
Significant (p<= 0.05) Slope; we have sufficient evidence to suggest that the slope is non-zero in the population. This evidence that the variables are related Intercept; we have sufficient evidence to suggest that the intercept is non-zero in the population. When X is zero, we expect Y to be different from zero Non-significant slope : we do not have sufficient evidence to conclude that the slope is different form zero in the population. This does not mean the variables are not related, but neither doe it provide evidence that they are. Intercept: We do not have sufficient evidence to conclude that the intercept is different from zero in the population Correlation is bounded (-1 or +1) because this denominator captures something about the total possible variance across the two variables; tells the max amount - the numerator must be equal to or smaller than that value The slope is unbounded
Estimating the slope and intercept
Simple linear regression equations Requires us to know the mean of X, the mean of Y, and the estimated slope (b1) Requires us to know the sum of products and the sum of squares on x
T- tests
Single sample design- used to compare the mean of one sample to the mean of a population One-group design- used to compare the means of two conditions in a within-subjects or matched-pairs design Two group design- used to compare the means of two groups in a between-subjects design
What do we do with a single sample mean?
Start by saying: what if my data is just the result of random sampling variation? What would my sampling distribution look like in that case? - how likely would I be to observe my particular sample estimate in that case> Estimate the probability of drawing that particular sample mean or something more extreme If the sampling distribution contains the set of all possible sample means, what proportion of those are >= (<=) the sample mean we've observed?
When to use correlation
T-tests/ ANOVA : categorical predictor (x) and continuous outcome (y) The categorical (nominal or ordinal) variable defines the group The continuous (interval or ratio) variable allows us to compute a mean for each group Chi- square (categorical predictor) (x) and categorical outcome (y) Cannot compute a mean of categorical variable Chi-square compares observed frequencies to expected frequencies Correlation/Regression: continuous predictor (x) and continuous outcomes (y) Not interesting to compare the means of two different variables Correlation assesses how consistently a change in X predicts a change in Y
You find that your new reading intervention improves reading comprehension compared to traditional instruction. Your effect size is d = 0.7. Which of the following is a correct interpretation of a Cohen's d of 0.7?
The average intervention group score was .7 standard deviations higher than the average traditional instruction group score. explanation: cohen's d is describing means, and the word "average"
Regression coefficient vs Correlation
The correlation coefficient is bounded between 1 and 1 because the covariance can never be larger than the square root of the product of the variance on X and Y The slope is unbounded because there is no limit on how much larger the sum of products can be relative to the sum of squares on X
What aspect of these diagrams below represents the between-group variance?
The distance between the means of the distributions
Statistical power
The power of a tst is the probability that the test will correctly reject a false null hypothesis. Power is the probability of detecting a real effect
A researcher conducts a study in which subjects complete a difficult search task in which they attempt to locate an X hidden among many Y's in a grid on a computer screen. Each subject completes this task under two "color" conditions: one in which the X is the same color as the Y's (e.g., both black) and one in which the X is a different color than the Y's (e.g., the X is green and the Y's are blue). The dependent variable is how long (in seconds) it takes each subject to locate the X in the two different "color" conditions. The researcher conducts a hypothesis test to determine if subjects are faster to locate the X in the "different color" condition than in the "same color" condition. Which analysis is appropriate for this hypothesis test? Explain how you know.
The two variables are continuous and categorical. Based on this we should be doing a T-test Anova, dependent/ paired sample t-tests. we are comparing means
Independent measures sample statistic
To compare these two conditions, we want to compare the difference between the sample means we've observed to what we think the difference between the population means would be if the null hypothesis is true
Dependent sample t-tests Within subjects
To compare these two conditions, we want to compare the mean difference score we've observed to what we think the mean difference score would be in the population if the null hypothesis is true Null hypothesis- in the population, the conditions are not different -> u1=u2 If u1=uz then ud=0 Ho; ud=0 then h1;ud=/ 0 So we're really asking: is the observed mean difference significantly different from zero? (i.e more than would be expected by sampling error alone?)
The use of z-scores
We can tell whether a score is high, low, or average from just z-score Equating and rescaling entire distributions Mean : always 0 Standard deviation : Always 1 Shape: Same as original distribution Making scores from non-equivalent distributions comparable A z-score of 1.2 has the same meaning, no matter what the original distribution Z-scores are " distribution-free unitis" The sampling distribution of sample means is normal Z-scoring a normal distribution gives us a unit normal distribution
Factorial Notation:
Written out like a multiplication expression # x # x # etc. Number of IVs = number of factors in the expression Number of levels in each IV= the specific value of each factor Number of conditions = the product of the factors Examples ; 2x2= "two by two"= 2 IVs, each with 2 levels= 4 conditions 3x3= " three by three" = 2 IVs, each with levels = 9 conditions
A researcher conducts a study in which participants played a "dictator" game, in which they were given points and asked how many they wished to allocate to a partner (a stranger) who had no points. Participants did not gain anything by allocating points to the partner, and in fact, giving points to this partner would hurt the participants' chances of winning the game. The researchers hypothesized that participants' altruism (operationalized as the points they allocated to the partner) would be related to their social class. To test this hypothesis, the researchers collected information about each participant's yearly household income (in dollars), in order to determine whether social class was predictive of altruism. What analysis is appropriate for this hypothesis test? Explain how you know.
Your Answer: They believe that social class will result is altruism. The operationalized social class through income in dollars. They operationalize altruism by the the points allocated. This gives us two continuous variables, giving us two continuous variable. Because there are two continuous variables, we would need to do correlation or regression analysis. Correlation would tell us how strongly they are related and Regression would tell us for a specefic dollar amount increase in income how many additional points would we expect to allocate.
Common test stats:
Z-test- comparing sample mean to population mean (sigma known) T (t-test) - comparing 2 means or comparing sample mean to population mean (sigma unknown) F (ANOVA)- comparing 2+ mean R (correlation - evaluating relationship between 2 quantitative variables x(squared) ( chi-square)- eluting relationship between 2 categorical variables
Independent samples t-test
a hypothesis test used to compare two means for a between-groups design, a situation in which each participant is assigned to only one condition
Why is it that repeated measures designs have more statistical power than between-subjects designs?
because the residual (unexplained) error is smaller in a repeated measures design
Pearson's chi square
e stands for expected and o represents observed and i (predictor) and J (outcome) are referring to levels of different variables of your predictor and your outcome We are finding the difference between an expected frequency and an observed frequency, squaring that difference, and the dividing it by the expected frequency
Haichen is interested in studying the effect of subtitles on EFL students' ability to learn from video. Participants in her study watch a lesson and see subtitles that are either in their native language (Mandarin) or the same language as the video (English), and the subtitles are also either full (word-for-word transcription of the audio) or abridged (highlighting just key words and phrases). Each participant watches one version of the video lesson and then takes a brief test to determine how much they have learned. Which type of analysis would be appropriate for analyzing the results of this design?
factorial Anova (between subjects)
A factorial design cannot have more than three independent variables.
false
If a design has no interaction, there will be no main effects either.
false
If the counselor wishes to determine whether the mean number of years of marital relationships for clients is significantly less than that for a group of nonclients, what statistical test is appropriate? Assume no pairing.
independent sample t-test
A researcher is interested in the effect of gender bias in hiring. A total of 100 scientists were given a fake job application and had to decide how likely they were to hire the candidate. 50 scientists received an application with a typically male name on top, while the other 50 scientists received an application with a typically female name on top. The applications were identical other than the name. The dependent variable was the scientists' rating of how likely they were to hire the candidate. Which hypothesis test would be appropriate to test the difference in rating between the male-name and female-name conditions? What would the null hypothesis be for the test in the previous question?
independent samples t-test or one-way Anova The mean rating is the same for the male-name and female-name conditions.
A school psychologist compares the reading comprehension scores of children of migrant farm workers who, as a result of random assignment, are enrolled in either a bilingual reading program or a traditional reading program.
independent- samples t-test
A researcher randomly assigns high school students to either a speed-reading training condition or a control condition and tests their reading comprehension just once at the end of the study.
independent- samples t-tests
A political scientist wishes to determine, in detail, whether males or females differ with respect to their support for the funding of energy conservation programs by the federal government. After being informed about the current budget for these programs, each person is asked to estimate, to the nearest $100 million, an appropriate level of spending.
independent-samples
Amir is conducting a study in which he shows participants one of three television commercials (charity, political, or control) in order to see which causes the most helping behavior. In this study, Amir is also interested in seeing how sex (male versus female) may interact with the type of commercial watched and affect helping behavior. Identify the number of main effects and interactions Amir will need to investigate in his study.
interactions - one main effects - two In this example, there could potentially be one interaction: between sex and type of video shown. There could potentially be a two main effects: one for type of video and one for sex. When there are two independent variables, this will always be the case.
Interpreting the Slope and Intercept
ntercept = the expected value for y when X is 0 From our example b0= 72.4 When students study for 0 hours, we expect them to get an exam score of 72.4, on average Slope = the expected change in Y for each 1-unit increase in X From our example : b1=1.77 For each additional hour of study, we expect exams scores to increase by 1.77 points, on average
If the counselor wishes to determine whether significant differences exist among the mean years of marital relationships for three randomly selected groups of clients with different ethnic backgrounds—African-American, Asian-American, and Hispanic—what statistical test is appropriate?
one -way between subjects ANOVA
A data-oriented marriage counselor, who works with clients in groups, might suspect that his clients' decision to seek counseling is attributable to the length, in years, of their marital relationships. If the counselor wants to determine whether, among the population of clients, the mean number of years of their marital relationships differs from a specific number, such as seven years, to evaluate the popularly acclaimed "seven-year itch" as a source of marital stress, what statistical test is appropriate?
one sample t -test
To determine whether a new sleeping pill has an effect that varies with dosage, a researcher randomly assigns adult insomniacs to receive either 0, 4, or 8 grams of the sleeping pill. The amount of sleeping time is measured for each subject during an 8-hour period after the administration of the dosage. one-way between-subjects ANOVA Correct!
one way between -subjects Anova
A psychologist uses chimpanzees to test the notion that more crowded living conditions cause aggressive behavior. The same chimps live in a succession of cages containing either one, several, or many other chimps. After several days in each cage, chimps are assigned scores on the basis of their aggressive behavior toward a chimplike stuffed doll in an observation cage. Which type of analysis is appropriate for this design?
one-way repeated measures analysis
When to use chi-square When we are doing observed frequencies
t-tests/ Anova : categorical predictor (x) and continuous outcome (y) The categorical (nominal or ordinal) variable defines the groups The continuous (intervals or ratio) variable allows us to compute a mean for each group Chi-square: categorical predictor (x) and categorical outcome (y) Cannot compute a mean of a categorical variable Chi square compared observed frequencies to expected frequencies
what is the appropriate interpretation of b1?
the expected change in Y for each one-unit increase in X explanation: in this model B1 is the slop. B1 is the rise to the run. Option A is talking about the intercept. Option B is referring to the mean of y. If you know x is at the mean, so is Y, in a regression line
(true of false) A main effect of an IV can also be referred to as an overall effect of an IV.
true
A cell in a factorial design table acts as a unique condition in factorial designs.
true
An interaction can be described as a difference in differences.
true
