PY301 Exam 1

Describe the difference between measurements and designs.

Measurements translate broad concepts into narrow data, and they are at the level of specific numbers. Designs are at the level of procedure, and they are bigger than measurements.

What does ANOVA stand for, and what does it do?

Analysis of variance; compares means

Name some differences found in a professional APA style paper.

Less information on a title page, running head, typically include an author’s note.

Describe the theory/data cycle.

Theory tells us where to look → data tells us what actually happened → theory tells us why something happened/makes sense of data → data tells us when/how to revise theory → repeat

What are some characteristics of a good research question?

Based on a personal or formal theory; specifies variables; does not start with Why; ends with a question mark; hypothesis is an initial answer

Briefly describe the three major designs in psychological research.

Observational/correlational: 2 or more variables measured at the same time; predictor and outcome variables
Quasi-experimental: no creation of groups, some idea that a preexisting variable is stable and not caused by a DV
Experimental: manipulation of an IV, hold all else constant

Rank the internal validity of correlational, quasi-experimental, and experimental designs.

Experimental > quasi-experimental > correlational

Name some types of measurement.

Behavioral/observation, physiological, survey/interviews; manipulation/intervention

True or false: Research is objective, especially research involving physiological measurements.

False

What are descriptive statistics?

Mathematical summaries of data; distributions of a single variable (e.g. measures of central tendency, variability)

What are inferential statistics?

Probabilistic summarization of data (e.g. hypothesis testing, probability)

What is the technical definition of probability?

The number of possible outcomes of interest divided by the number of total possible outcomes.

Briefly describe randomness.

Each member of a population has an equal probability of being assigned to a group (random assignment) or being selected (sampling).

What percentage of data points in a normal distribution are within 1, 2, and 3 standard deviations of the mean?

68%; 95%; 99.7%

Populations are _______ ____, samples come from _______.

Infinitely large; populations

What is the notation of populations and samples, respectively?

Greek; Roman (normal English)

As n increases, what happens to the sample mean?

Sample mean will be closer to population mean, outliers have less weight on the sample mean (more stability).

Conceptually, what is standard deviation?

The standard distance that a point will deviate from the mean.

Conceptually, what is standard error?

The typical distance that a sample mean deviates from the population mean.

What is standard error?

The difference that a sample mean deviates from the population mean (μ - M)

Write the formula for the standard error.

σ/√n

In science, the burden of evidence is placed on…

The researcher

What is the question associated with p-value?

If the null hypothesis is true, what is the probability that my data would be at least as extreme as they are?

Define Type I and Type II errors.

Type I Error: false positive, finds something significant that is not there (defined by alpha, .05)
Type II Error: false negative, concluding no effect when there is an effect (can’t quantify)

What can drive down Type II error rates?

Increasing sample size, bigger effect size, increase type I error rate

Effect sizes are similar to computing the statistic of interest, but they ignore…

Sample size

Statistical significance is determined by _____, which is determined by _____ ____ and _________ __ _ _______.

p-value; sample size and distribution of a statistic

What is variance?

Standard deviation squared (no conceptual idea)

What are some problems with relying on p-values alone?

Can distract from meaningful significance; assumption of just one test; problem of categorical thinking; not a measure of relationship strength

What are the steps to calculate variance?

1. Subtract the mean from each score

2. Square each deviation

3. Sum the squared deviation (the SSD)

4. Divide the SSD by the degrees of freedom (number of scores - 1)

What distributions do the standard deviation and the standard error belong to, respectively?

Any distribution (typically normal distribution); sampling distribution of the mean

The sampling distribution of the mean is a distribution of a _______ ______, not _______ ____.

Descriptive statistic; individual cases

What are some elements of the central limit theorem?

We never have the population or sampling distribution; the distribution of sample means is normal if n or the population is normal; centered on the population mean; has standard error of σ/√n

True or false: The principles of hypothesis testing revolve around the assumption that we are wrong until demonstrated otherwise.

True

What is meaningful significance determined by?

You, and effect sizes

All ANOVAS use what types of independent and dependent variables?

Categorical; continuous

Do we always assume that an ANOVA is between-subjects or within-subjects?

Between-subjects

If the null hypothesis of a one-way ANOVA is true…

The variance between group means is roughly equal to the variance within groups (effect = error); variation between group means does not have to be zero.

What does F tell us in an ANOVA?

Whether one or more levels is different from one or more levels

True or false: A significant p-value and effect size evaluation is the endpoint in a multi-level ANOVA.

False; post-tests are needed

What are some examples and impacts of artificially categorical data?

High vs. low social pressure to cheat on honesty behavior, introverts vs. extroverts on relationship satisfaction; limits IV variability, limits ability to see non-linear relationships

What distinguishes methods from statistics?

Method determines validity, and we are able to draw causal inference determined by measures and procedures; statistics tell us whether there is a relationship, its strength and direction, and the quantitative nature of the relationship

What is the conceptual formula for r?

Degree to which X and Y vary together divided by the degree to which X and Y vary separately

What distinguishes correlation from regression?

Correlation tells strength and direction, regression tells nature and provides a prediction

What are the predictor and outcome variables in the following observational study: Number of years employed and job satisfaction.

Predictor: number of years employed
Outcome: job satisfaction

What are some examples of descriptive statistics?

Measures of central tendency (mean, median, mode), variability, spread of data

What is the question associated with hypothesis testing?

What can I infer about a population from sample data?

Inferential statistics often examine…

The relations between variables

Why is the distribution of the sample mean narrower than the original population mean?

The averaging effect; extreme values have less of an impact on a sample mean the larger the sample size is.

As n gets larger, does SE increase or decrease? Think of the SE formula.

SE decreases

What is a conceptual way of understanding p?

The area under the curve at least as extreme on both tails of a sampling distribution.

What is the formula for variance?

s² = Σ(X-M)²/ N-1

Why do we subtract one to find degrees of freedom?

We do not like redundant information when dealing with probability.

What is the formula and conceptual understanding for SSwithin?

ΣSSinsideeachtreatment; sum of every group SS

What is the formula and conceptual understanding for SSbetween?

nΣ(M-GM)² [M = group mean, GM = grand mean); sum of all groups’ squared deviations from the grand mean multiplied by the number of individuals in each group

What is the formula and conceptual understanding for dfwithin?

N - k (k = number of groups); number of data points subtracted by number of groups

What is the formula and conceptual understanding for dfbetween?

k - 1; number of groups subtracted by one

What is the formula and conceptual understanding for r²?

SSbetween/SStotal; the percentage of variability in Y explained by X

What is the formula for all MS values?

SS divided by df

What is the formula and conceptual understanding for SSsubjects?

kΣ(MP-GM)²; number of groups multiplied by the groups’ squared deviations from the grand mean

What is the formula and conceptual understanding for dfsubjects?

n - 1; number of individuals subtracted by one

What is the formula and conceptual understanding for SSerror?

SSwithin - SSsubjects; a measurement of how much actual data points vary from what is predicted (low SSerror indicates better predictions)

What is the formula and conceptual understanding for dferror?

dfwithin - dfsubjects; number of independent pieces of information that vary due to unexplained variability in the data

What is the formula and conceptual understanding for F in a repeated measures ANOVA?

MSbetween/MSerror; variance between treatments divided by variance due to error, taking individual differences into account

What is the formula and conceptual understanding for F in a between-subjects ANOVA?

MSbetween/MSwithin; variance between groups over variance within groups

What are some post-tests used for ANOVAs?

Scheffe (Jason thinks it’s sketchy), Tukey’s HSD, Bonferroni

What does a significant p-value and effect size indicate for an ANOVA?

One or more conditions is significantly different from one or more other conditions.

What are the steps for computing a repeated measures ANOVA?

1. Calculate SSs and dfs as in a between-subjects ANOVA.
   2. Remove the individual differences from SSwithin by subtracting SSsubjects from SSwithin, giving SSerror.
   3. Calculate F by dividing MSbetween by MSerror.

What are r-values indicating an extremely strong, average, and no relationship?

0.6, 0.3, 0.0

Write and describe the formula for r.

SP/√SSXSSY; the sum of a point’s deviation along X and Y [Σ(X-MX)(Y-MY)], divided by the square root of the product of variability in X and Y independently.

What is the df for r, and why is it like this?

N - 2; you lose a df every time you calculate a mean, and there is no group size in r.

What is the formula for the slope of a line when using regression?

Ŷ = a+bX (b = regression coefficient, a = constant, Ŷ = predictive value of Y)

What are the formulas for b and a for a regression line? Explain them both conceptually.

b: SP (sum of products)/SSX; scales covariation to the units of X to influence how the line sits.
a: MY-bMX; shows the increase in Y for each 1-point increase in X

What are the interpretations of the values in a regression line equation?

b = Y-value at zero; a = increase in Y for each 1-point increase in X; Ŷ = predictive value of Y

What are the technical and conceptual formulas for F in a regression model?

MSregression/MSresidual; predicted variability in Y/unpredicted variability in Y

What are the formulas for SSregression, dfregression, SSresidual, and dfresidual, all used in regression calculations?

SSregression: r²SSY (predicted variability * total variability)
dfregression: 1
SSresidual: (1-r²)SSY
dfresidual: n - 2
(SSregression + SSresidual = SSY)

What are some differences between r and r²?

r is a measure of relationship strength and it bound by negative 1 to 1; r² is the percentage of variability in Y explained by variability in X, and it is bound from 0-1.

What is the formula and conceptual understanding for η², the effect size for ANOVAs?

SSbetween/SStotal-SSsubjects; the proportion of variance in a dependent variable that is attributable to an independent variable or factor

When would you use the Scheffe, Tukey’s HSD, and Bonferroni post-tests?

Scheffe: almost never
Tukey’s HSD: Most common, use when only pairwise comparisons are made (sets a threshold for significant differences in the units of the raw data)
Bonferroni: Use for general tests of possible contrasts, small set of planned comparisons (conduct a series of t-tests/ANOVAs with two levels, divide alpha level by number of comparisons)

Two numbers are drawn from two different distributions. One of those numbers is closer to the mean of its distribution than the other. If you had to bet on which distribution has the number that is closer to the mean, which would it be?

I would bet that the distribution with less variability would have the number closer to its mean. A distribution with less variability has a smaller standard deviation, thus the typical point is closer to the mean.

What is the shape of the F distribution, and why is it shaped this way?

There is a big peak at F=1, it is bounded by zero, and it is positively skewed. Since the calculations needed to find F are sums of squares, these values must be positive, thus no values of F can be positive, and squaring scores causes negative scores to be flipped and “stack up” on the positive side of the distribution. Furthermore, if the null hypothesis is true, SSbetween will equal SSwithin, thus the majority of points will fall around F=1, and it is increasingly rare for points to fall further away from 1.

If X and Y are strongly positively correlated, what happens when you calculate their differences and multiply them together?

When X is above MX, Y is also likely above MY, and vice versa. Thus, you will always get a positive sign when solving for SP, creating a positive r value. Additionally, pairing large deviations with small deviations produces a medium-sized number, emphasizing the simultaneous existence of the larger and smaller variations within the same relationship.

If X and Y are strongly negatively correlated, what happens when you calculate their differences and multiply them together?

When X and Y are strongly negatively correlated, their signs will be different, thus, a negative number will be produced when calculating SP, indicating the negative relationship. If a large negative deviation is paired with a small positive deviation, a medium-sized negative SP will be calculated, which combines the overarching negative trend of the relationship. The same thing happens with a small negative deviation and a big positive deviation.

If X and Y are not particularly correlated, what happens when you calculate their differences and multiply them together?

When X is above MX, the associated Y value may be above or below MY, thus the signs with be inconsistent when you calculate the differences in means and multiply them together, producing an SP close to zero, emphasizing the lack of a significant correlation.

Suppose you calculate a high r and F value and create the following regression line for sleep and performance on a test: Ŷ=53.17+0.09X. Interpret this equation.

When an individual sleeps zero minutes before a test, we can predict that their score will be 53.17 points. For every additional minute slept, we can predict that an individual’s score on a test will improve by 0.09 points. The high r and F values tell us that there is a significant positive correlation between these two variables, and we can confidently predict that test scores will increase as the number of minutes slept increases.

What does an ANCOVA do?

Adds covariate(s), calculates the degree to which covariates overlap with/predict DV, removes this overlap and runs ANOVA with clean variables