psych 2016 chapter 11 - psych stats

F distribution

-The distribution of possible outcomes for the test statistic, is positively skewed - is derived from a sampling distribution of F ratios

Pearson correlation coefficient

-The value in the numerator reflects the extent to which values on the x-axis (X) and y-axis (Y) vary together -the extent to which the values of two factors vary together is called covariance -The extent to which values of X and Y vary independently, or separately, is placed in the denominator

ways population variance might be provided

-compared to the general population with a mean of 3 and standard deviation of 1 -versus the population of men in general, m=3 deviation =1 -population with a men of 5 and a variance of 2 -population parameters m=3 , deviation squared =1

frequency tables

-group vs ungrouped styles of organization !. Grouped is for larger groups of data, divided into intervals -Find real range - find interval width -construct frequency distribution 2. Ungrouped is for a discrete range of values that allows you to see raw data interval width and creating intervals for grouped data -relative/ cumulative frequency/ percentage -relative frequency: %in which decimal form to show the % of people in that interval -cumulative frequency: at which interval how many people were observed

post hoc test

-statistical procedure computed following a significant ANOVA to determine which pair or pairs of group means significantly differ -necessary when k>2 because multiple comparisons are needed

how many times was the participant observed on the outcome

1 time? -between subjects more than 1 time? -within subjects (aka repeated measures)

Assumptions of 1-way between subjects ANOVA

1. Normality- assume that data in the population or populations being samples are normally distributed 2. Random sampling- assume data measured were obtained from a sample that was selected using a random sampling procedure 3. independence- assume that the probabilities of each measured outcome in a study are independent or equal 4. Homogeneity of variance-assume that the variance in each population is equal to each other

common methods of research

Correlational: observing variables to see if they have a relationship Experimental:cause and effect Manipulate the IV Randomization Comparison/control Quasi-Experimental: experimental without meeting all the requirements

According to lecture which measure of effect size will we be using for both types of one-way ANOVA?

Eta Squared

F statistic or F obtained formula

Fobt=MSbg/MSe

Post hoc tests are computed ______.

Following a significant ANOVA test to make pairwise comparisons.

Q2: How many factors?

If we are talking about between group differences in means, factors are the grouping variable(s) being used to predict the outcome of interest Does life expectancy differ by highest degree earned -1 factor Does life expectancy differ by highest degree earned and socioeconomic status -2 factors

F statistic or F obtained

It os a ratio of the variance explained by the treatment (Between treatment variance) compared to the variance not explained by the treatment (within treatments variance). it is computed as mean square between groups divided by mean square within groups

Q1: What is the research question asking?

Mean difference- we are looking at group differences on a continuous measure "a researcher is interested in whether AP students have a different IQ that the general population"- comparing sample mean to known population mean "a research is interested in whether adolescents and adults have different stress levels" - comparing sample mean to sample mean

scales of measurement

Nominal variables assign numbers to qualitative and discrete categories -sex (male=0, female=1) -favorite color (blue=1, orange=2, purple =3) ordinal variables capture the rank ordering of categories -ranking of athletics in competition (1=1st, 2=2nd) Letter Grades (A,B,C,D,F)

How many groups are samples

One group: a researcher is interested in whether AP students have a different IQ than the general population (M=115). Two groups: A researcher is interested in whether adolescents and adults have different stress levels more than two groups: A researcher is interested in whether people with different pets report higher life satisfaction

A researcher assigns 21 adolescents to rate the likability of a person described in a vignette as having one of three personality traits. An equal number of participants are assigned to each group. Based on the results, F(2, 20) = 4.08, p<.05, what was the decision for a one-way between-subjects ANOVA?

Reject the null hypothesis

Q1: What is the research question asking?

Relationship- we are looking at how to variable covary with one another "A researcher is interested in whether there is a relationship between severity of traffic and mood" "a researcher is interested in whether severity of traffic predicts mood"

ANOVA table

SS: sum of squares df: degrees of freedom K: number of groups N: total sample size MS: mean square - ss/df for each line F: test statistic

F distribution

The F distribution is a family of distributions with many possible F distributions. Like the other distributions we have worked with, it helps us to determine the area of rejection. • The shape of the distribution depends on df numerator and denominator • The shape is skewed positively• The distribution can only contain values ≥ 0

To summarize a one-way within-subjects ANOVA, we report each of the following except, ______.

The critical value

F statistic

The variances measured in an ANOVA test are computed as mean squares (MS), or variance

z-score transformation

We can take raw scores, calculate a standardized z-score and then use this z- score to find the proportions/area/probability between the mean and the z- score (column b) or the z-score and the tail (column c) in the unit normal table. • Raw score→z-score→Unit normal tableWe can also start with a proportion/percentage/area of interest and work backwards:• Unit normal table→z-score→raw score

Family-wise error rate

When comparing means of multiple groups, pair by pair using a t-test, this error rate is the probability of falsely rejecting the null hypothesis in either one of those tests.

A professor compared differences in class grades between students in their freshman, sophomore, junior, and senior years of college. If different participants were in each group, then what type of statistical design is appropriate for this study?

a one-way between-subjects ANOVA

population parameters

an entire group of people (inferential)

calculating slope and intercept

b = changes in y/ changes in x = ssxy/ssx a=My-bMx

A psychologist is studying the influence of pop music on test scores

causal

A researcher is interested in whether happiness increases work productivity

causal

Following a significant one-way between-subjects ANOVA in which k = 4, what is the next appropriate step?

conduct a Tukey HSD post hoc tes

A researcher measures anxiety levels and cortisol to test if there is a relationship. What type of statistical design is appropriate for this study?

correlation

A researcher measures cups of coffee consumed daily and daily work schedule to see if they are related. What type of test is most appropriate?

correlation

inferential statistics

data you can draw conclusions from, parametric, derived from probability theory (how the data behaves)

scales of measurement

discrete: separate and indivisible categories continuous: along a continuum quantitative: quantity/ numbers qualitative: by class normal: qualitative and discrete, used for categories or labels (gender) ordinal- quantitative and discrete, used for rankings (a,b,c or 1st, 2nd..) Interval-quantitative, even intervals with no meaningful zero (ACT scores) Ratio: quantitative, even intervals and meaningful zero (income, height)

effect size

effect size is variance explained , "eta squared" expressed as a percentage SSbg/SSt

The term "between-subjects" refers to ______

having different participants in each group and each participant is tested only once

Central Limit Theorem

he mean calculated across all samples would be normally distributed. Regardless of the distribution of scores in a population, the sampling distribution of sample means selected from that population will be approximately normally distributed ◦ At least 95% of possible Ms one could select fall within 2 SDs of μ (Empirical Rule)

A researcher measures differences in recall between male and female participants. What type of statistical design is appropriate for this study?

independent sample t test

Types of Variables

independent, dependent, controlled

scales of measurement continued

interval variables assign numbers with quantitative value with any two adjacent score having equivalent intervals. In these scales, there is no meaningful zero. -SAT/ACT scores -Temperature in Fahrenheit Ratio variables assign numbers with quantitative value with any two adjacent scores having equivalent intervals. In these scales, there is a meaningful zero -Income -Number of errors made

Without changing the value of error variance, the ______ the between-groups variability, the more likely we are to reject the null hypothesis.

larger

A researcher is interested in whether the severity of a cold causes an increase in the use of tissues. They measure number of tissues used and self-reported cold severity. What type of test is most appropriate?

line regression

What is statistics?

mathematical procedure used to summarize/analyze/observe data

central tendency and different ways to measure it (mean/ median/ mode)

metric to understand the center distribution in a data set mean: average median: middle # mode:most frequent #

A psychologist is curious if likelihood to be a CEO is predicted by extraversion (high-low), openness (high-low), agreeableness (high-low), neuroticism (high- low), conscientiousness (high-low). What type of test is most appropriate?

multiple regression

A researcher is curious whether the outdoor temperature is associated with number of hours slept each night

non causal

A student is researching how caffeine intake is related to insomnia

non causal

A researcher is curious whether the mean ratings of liking for a new food are greater than the ratings of most foods ( = 0)

one sample t test

A researcher compares differences in positivity between participants in a low-, middle-, or upper middle-class family. She observes 15 participants in each group and compares the average level of positivity in each group. What type of test is most appropriate for this study?

one way between subjects ANOVA

A professor compares scores on a competency exam among students at three times during a single semester. What type of test is most appropriate for this study?

one way within subjects ANOVA

A researcher wants to test if stress levels among nurses are higher compared to stress levels in the general population ( = 4). What type of test is most appropriate for this study?

one-sample t test

Is causal order determined?

only this question for the relationship side of the tree words that indicate NO causal order: relationship, association, related to, associated with, correlates with words that indicate causal order: causes, is affected by, predicts, is predicted by, is the result of, is influenced by, increases, decreases, improves, diminishes

A professor compares scores on a competency exam among students at two times during a single semester. What type of test is most appropriate for this study?

related samples t test

A researcher placed male rodents in the presence and absence of a male rodent of the same species. Mean cortisol (a stress hormone) levels of the rodent were compared at both times. What type of test is most appropriate for this study?

related samples t test

method of least squares

statistical procedure used to compute the slope (b) and y-intercept (a) of the best fitting straight line to a set of data points To use the method of least squares, complete three steps: ◦ Step 1: Compute the preliminary calculations ◦ Step 2: Calculate the slope (b)◦ Step 3: Calculate the y-intercept (a) y(predicted y value)=bX(slope)+a (y intercept)

sample statistics

subset of population (descriptive)

descriptive statistics

summarize data, non-parametric (how the data works)

Homogeneity of variance is an assumption for the one-way between-subjects ANOVA. What does this assumption mean?

that the variance is equal in each population from which samples are selected

picking the correct test- decision tree

the decision tree is useful for identifying inferential statistics not descriptive statistics

For an analysis of variance, the term "one-way" refers to ______.

the number of factors in a design

A lowercase k is used to denote ______ using a one-way ANOVA.

the number of groups in a study

Computing a one-way between-subjects ANOVA is appropriate when ______.

there is one factor with three or more levels and different participants observed in each level

What is the goal of statistics in behavioral research?

to conduct quantitative analyses

A psychologist is curious how memory is impacted by time of day (morning vs afternoon, vs evening vs night) and familiarity with the setting (familiar vs unfamiliar setting). The psychologist samples 400 participants and assigns them to one time of day and one level of setting familiarity to perform a memory task. They then compare memory levels between groups. What type of test is most appropriate to test this scenario?

two way ANOVA

correlation coefficient

used to measure the strength and direction of the linear relationship, or correlation, between two factors The value of r ranges from −1.0 to +1.0• Values closer to ±1.0 indicate stronger correlations • A value of 0 indicates no relationship o The sign of the correlation coefficient (− or +) indicates only the direction or slope of the correlation

post hoc test comparisons

when the ANOVA is significant, conduct post hoc test

The source of variability associated with error variance in the one-way between-subjects ANOVA is called ______.

within-groups variability

A professor finds that the average SAT score among all students attending his college is 1150 ± 150 ( ± ). He polls his class of 25 students and finds that the average SAT score is 1,200. What type of test is most appropriate for this study?

z test

A researcher selects a sample of 36 students from a school population (105 ± 12). She determines that the mean IQ in this sample is 104. What type of test is most appropriate for this study?

z test

should I do a z test or a t test?

z test uses standard error of the mean which is calculated with the population variance t test uses estimated standard error of the mean which is calculated with the sample variance (because population variance is unknown)

sampling distribution

• Sample Design• Theoretical vs experimental sampling: What are they? Which is used more in the real world? Don't need to calculate for exam. Sampling distributions. What are they? Central limit theorem. Standard error of the mean: what is it? What does it measure? How do you calculate it? Interpreting z scores in sampling distributions