Research Design & Statistics: Chapters: STATS 7-9/ R.M. 7

What are 5 things that affect Power? (increase power)

1)Use a higher alpha level (e.g., 10% instead of 5%)(generally a bad idea) 2)Use a one-tailed hypothesis instead of a two-tailed hypothesis. 3)Increase sample size (N) 4)Somehow make the difference between population means bigger. (e.g., stronger manipulation of IV) 5)Somehow reduce standard deviations in the populations. (e.g., from extraneous variables)

What are three things that Power depends on?

1. Criterion for statistical significance (aka alpha, e.g., .05) 2. Effect size 3. Sample size.

What are some questions you should ask when organizing your data for analysis?

1. What TYPES of data are the independent and dependent variables? 2. How is the dependent variable being measured? 3. How is the independent variable being measured?

What are some ways to eliminate confounding variables and minimize the effects of extraneous variables?

1.Control the variable: hold it constant •Environment: Task, setting, etc. •Participant variables: match 2.Random Assignment (between-Ss design) 3.Within-subjects design

What are the four steps of Hypothesis Testing?

1.State two hypotheses. 2.Set criteria for making a decision (find "critical region" of sampling dist.) 3.Collect data and compute test statistic (e.g., z, t, F, χ2) 4.Make decision about the null hypothesis (reject, or fail to reject)

What is a Confounding Variable?

A 3rd variable that systematically covaries with the IV and therefore may be responsible for any pattern we see in the DV... it is LOCKED ONTO the IV

What is Sampling Distribution?

A HYPOTHETICAL distribution of MEANS (or other statistics), rather than a distribution of individual scores. It corresponds to a particular hypothetical population distribution with mean mu and SD sigma. It is the distribution of means that you'd get from that particular population if you re-sampled a bazillion times (with the same sample size every time)

What is a confounding variable?

A confounding variable is a factor other than the independent variable that causes a change in the dependent variable.

The sampling distribution for the t-test is what?

A distribution of t-scores and its shape will be a t-distribution. (The exact shape depends on the df)

What is the Ratio Scale of Measurement?

A mathematical comparison between two numbers. When ratios are compared (and divided), the answer is the comparison, not the variable. Ratios of different units cannot be compared

What are the comparisons of One-Tailed and Two-Tailed tests?

A one-tailed test allows rejecting the H0 when there is a relatively SMALL difference in the specified direction. A two-tailed test requires a relatively LARGE difference regardless of the direction. it is the more statistically conservative (safe) approach. # of tails only changes the zcritical (and p-value), won't change the test stat (z).

What is Temporal Precedence?

A process that establishes what comes first: the cause or the effect. IV comes before DV

What is Correlation?

A recognized relationship between two things or events, but it does not imply causation.

What is a random sample?

A sample in which each member of the population has an equal chance of being selected for the sample.

In statisitcs, a sample is:

A set of data taken from the population to represent the population.

What is Hypothesis Testing?

A statistical method that uses sample data to evaluate a hypothesis about a population.

What is the Law of Large Numbers?

A theory of probability that states that the larger a sample size gets, the closer the mean (or the average) of the samples will come to reaching the expected value.

Each participant experiences just one level of the IV is which type of design: Between or Within Subjects?

Between-subjects Design(aka Independent Groups)

How do you demonstrate an understanding of an experiment?

By organizing and critically analyzing the data.

Variables are collected in the form of data. What are two major forms of data?

Categorical and Quantitative

What is Nominal Scale of measurement?

Categorical data that assigns numerical values as an attribute to an object, animal, person or any other non-number. CANNOT be ordered. The numbers themselves have no value, they simply identify characteristics.

What are some examples of the Nominal scale of measurements?

Color of the sunset for today. Gender, Political affiliation

What are theories in psychology that can't really be measured directly?

Constructs

What is the group called that is untreated throughout an experiment?

Control Group

What is information that is collected for analysis?

Data

What is Ordinal Measurement?

Data that CAN be ordered and ranked, but not measured. It cannot be multiplied, divided, added, or subtracted.

What is Interval Measurement?

Data that is grouped in evenly distributed values and measured based on the group to which that variable is attributed. This is the most powerful scale of measurement. There are no meaningful zeros. It uses the mean.

What is the piece of data in an experiment that is controlled or influenced by an outside factor, most often the independent variable.

Dependent Variable

How do descriptive and inferential statistics differ?

Descriptive statistics only attempt to describe data. (Sample) Inferential statistics attempt to make predictions based on data. (Population)

What are the three main types of research methods?

Descriptive/observational Correlational Experimental

Experiments are the only way to__

Determine cause and effect relationships

What is it called when a graph or a table is used to helps us interpret our data?

Distribution

Between-subjects design

Each set of scores is obtained from different groups of participants. t-test: You compare condition means BETWEEN the two groups.

What characteristic(s) must a sample have in order to be considered a random sample?

Every member of the population must have an equal chance of being selected to be a part of the sample AND the selection of one member of the population is not dependent upon the selection of another member.

What are Experiments?

Experiment (true experiment)- Must demonstrate that the changes in one variable are directly responsible for causing changes in the second variable Big Idea: We systematically CHANGE (manipulate) one variable (IV),and see (measure) what happens to another one (DV). The most powerful tools in our arsenal to understand the truth of reality Causality

What are the two groups used when running an experiment to test for an independent variable?

Experimental group & control group

What is it called when the results of an experiment are true in the outside population? The extent to which a study's results can be generalized beyond the study is what? How consistently a method measures over time when repeated is what?

External Validity

Katie asks the 25 students in her class what their favorite color is and records their answer. She puts this data into a table. Which kind of distribution would Katie have?

Frequency Distribution

What is Standard Error (SE)?

How far we can generally expect sample means to be from the population mean.

What is covariance?

How two sets of variables behave in relation to each other. Is there a significant difference of DV between conditions of the IV?

Why do we do hypothesis testing?

Hypothesis testing is about testing to see whether the stated hypothesis is acceptable or not. During our hypothesis testing, we want to gather as much data as we can so that we can prove our hypothesis one way or another.

What is HOMER?

Hypothesize Operationalize Measure Evaluate Revise, Replicate, Report

What is the shape of the Sampling Distribution?

If the population distribution is NORMAL shaped: •The Sampling distribution is normal (for any n) If the sample size (N) is LARGE: •The Sampling distribution approaches normal

Many kinds of data we collect in psychology fall into a normal pattern, as explained by the central limit theorem. This means that ____

If you have a large enough sample, the distribution of most data will be approximately normal.

Why is it important to know the limits of an experiment?

In order to analyze and infer information about the experiment, you have to know exactly what the experiment can tell you and what it can't.

What would happen if you increased alpha (e.g., from .05 to .10)?

Increase the chance of Type I Error (false positive), and increase power

What are two sources of Confounding Variables?

Individual Differences Environmental Variables

What is it called when an experiment measures the variable that it was designed to measure & The ability of the researcher to say that only the independent variable caused the changes in the dependent variable?

Internal Validity

What is data that is grouped in evenly distributed values and measured based on the group to which the variable is attributed?

Interval measurement

How can you reduce the probablity of getting a Type II Error?

It can be decreased by making sure that your sample size is large enough so that real differences can be spotted.

How is the Standard Error useful?

It helps us decide if a sample mean we got is IMPROBABLE for a given population mean.

What is a Significance test?

It tells us how much we should believe in the real existence of an effect. ex: p = .035

What are some advantages of Random sampling?

It's highly representative of the population. (external validity) It decreases bias since the process of selecting the sample is done randomly. Data analysis and interpretation is simpler in random samples

What are some disadvatages of Random Sampling?

It's not possible if you do not have a complete list of the members in the population. It can take a lot of time and money if you are sampling data from a large population. The characteristics of the sample and/or the population can change over time.

What are some examples of the Ordinal Scale of Measurement?

Levels of achievement, prizes, rankings, and placements. Air quality status report for today: Very bad, bad, okay, good.

What are the characteristics of the t distribution?

Like the normal (z) distribution, t distributions are symmetrical and centered on 0. The t distributions have greater variance than the normal. (Wider, and fatter tails) The exact shape of a t distribution depends on the SAMPLE SIZE (or rather, df). With bigger and bigger sample sizes, the t distribution gets closer to a normal shape

What are some examples used in Descriptive Statistics?

Mean (average) Standard Deviation Bar Graph Frequency Table

What are two examples of descriptive statistics?

Mean and Standard Deviation

What do these symbols represent? M or X ̅

Mean of a Sample

What is a statistical estimation?

Methods for reducing errors in inferential statistics.

What is an example of a contruct?

Motivation

Within-subjects design

Multiple sets of scores are obtained from the same group of participants. t-test: You compare condition means WITHIN each participant.

What are the requirements for a study to be an experiment?

Must have Independent and Dependent variables

What kind of skewed distribution is it where the values are on the left of the graph and the scores fall above the mean.

Negative Skew

Is Correlation sufficient to demonstrate causation? How is causation determined?

No. Controlled Experiments

The numbers on lacrosse jerseys are an example of what kind of data?

Nominal

What is NOIR?

Nominal Ordinal Interval Ratio

In correlational research how are the Scales of Measurement measured?

Nominal- contingency table, Chi-Square test. Ordinal- Correlation (rho) Interval/Ratio- Pearson's Correlation & Regression

In an experiment, what scale of measurement is used for the Independent Variable and what tests are used?

Nominal- uses t-test, ANOVA Interval/Ratio- uses Correlation, regression.

What is the most common type if distribution? What is another name for this type of distribution?

Normal Distribution Bell Curve

A coach records the levels of ability in martial arts of various kids. What type of data is this?

Ordinal

What are the characteristics used to describe a population?

Parameter

What are the three types of distributions?

Population Sample Sampling Distribution

What is the difference between population and sample?

Population is all members of a defined group that have certain characteristics or attributes that we are interested in studying. Sample is the part of a population used to describe the whole group or entire population.

Martin has a large dataset and is doing some calculations. He displays his data in a graph and it is very unusual because many of the data points fall below the mean. This is a _____.

Positively skewed distribution. Positive Values are to the right.

What are the three types of order effects?

Practice Fatigue Carryover

A normal distribution is also a _____

Probability distribution

What does random assignment in experimental designs do?

Random assignment gives each participant in the experiment an equal chance of being in the experimental group and helps to eliminate confounding variables (internal validity). Only relevant for experiments

What is the method used to choose members of a group to participate in an experiment?

Random selection

What is a mathmatical comparison between two numbers?

Ratio

What is the extent to which the findings can be repeated and is consistent?

Reliability

What are the synonyms for Sampling Distribution (of the mean)?

Sampling Distribution Distribution of Means Distribution of Sample Means Sampling Distribution of the Mean

What are the three types of t-tests?

Single Sample Two independent samples (between subjects) Two related samples (within-subjects)

What is the Central Limit Theorem?

States that the more an experiment is run, the more its data will resemble a normal distribution. The variance and the standard deviation will DECREASE. The bigger the sample size the skinnier the sample distribution. It's the cornerstone of Inferential statistics. For any population with mean µ and standard deviation σ, the distribution of sample means for sample size n will have a mean of µ and a standard deviation of σ/√n and will approach a normal distribution as n approaches infinity.

What are the characteristics of a sample used to infer information about the population?

Statistic

What is Sample Mean?

The average of all the guesses will approach the expected value as the sample becomes larger and larger.

Effect size (e.g., Cohen's d)

The bigger the effect size, the farther apart the means of the two sampling distributions will be. (and/or skinnier distributions). not affected by N.

Power (1 - β)

The bigger the power, the greater the chance of us detecting a real effect when one exists. This is influenced by the distance between the two sampling distributions, how skinny/fat they are, and the alpha level

What are the characteristics of sample size (N)?

The bigger the sample size, the skinnier the sampling distributions will be, which gives us a LARGER test statistic (e.g., z, t)

What is Power?

The likelihood that a study will yield a statistically significant result when the IV really has an effect. Power is an aspect of statistical validity

alpha (α)

The max probability of Type I Error (false alarm) that we're willing to accept. p-value must be less than alpha to reject null hypothesis. The criterion that a p-value must be lower than for us to conclude statistical significance. most often, α = .05

What is Causation?

The relationship between cause and effect.

What is a Two-Tailed Hypothesis Test?

The standard hypothesis testing procedure is called a two-tailed (nondirectional) test because the critical region is divided between the two tails of the distribution

Cohen's d effect size

The standardized difference between the means of two population distributions. ranges from 0 to >3 (∞)

When you measure something, the value you get consists of:

The true value of the variable +/- measurement error

Why do we want to reduce variance?

There is less overlap of the distributions and a better chance of detecting difference in means

What is a Type I Error?

This type of error happens when you say that the null hypothesis is false when it is actually true. (False Alarm) a(alpha) we generally use .05 which means that you are okay with a 5% chance of making a type I error. The lower the alpha number, the lower the risk of you making such an error.

What is a Type II Error?

This type of error happens when you say that the null hypothesis is true when it is actually false. (Miss)

What is an example of an Interval Scale of measurement?

Time, Temp, Likert Scale, GPA, IQ, SAT score.

What is an example of a Ratio Scale of Measurement?

Today's pollen count in number of milligrams of pollen per cubic meter of air.

What is an extraneous variable?

Uncontrolled, "nuisance" variables that could affect DV scores, but that does NOT covary systematically with IV condition.

Why might a researcher use a sample rather than an entire population for their study?

Using a sample is more practical than using an entire population.

In an experiment, what scale of measurement is used for the Dependent Variable and what tests are used?

Usually Interval/Ratio- uses Correlation, Regression, t-test, ANOVA Nominal- uses Chi-Square Test.

What is a One-Tailed Hypothesis Test?

When the researcher has a specific prediction about the direction of the treatment effect In a directional (one-tailed) hypothesis test, the researcher specifies either an increase or a decrease in the population mean as a consequence of the treatment

t-test

When we DON'T know the population mean (μ) and standard deviation (σ) Instead of the sampling distribution being normal-shaped, it'll be a slightly different shape, which will depend on df (which is based on sample size)

What is Negative Correlation?

Where the independent and dependent variables in a data set either increase or decrease OPPOSITE from one another.

What is Positive Correlation?

Where the independent and dependent variables in a data set increase or decrease TOGETHER.

Each participant experiences all levels of the IV is which type of design: Between or Within Subjects?

Within-subjects Design(aka Repeated Measures)

In which type of design: Between or Within Subjects has problems with Order Effects?

Within-subjects Design(aka Repeated Measures)

In which type of design: Between or Within Subjects is more efficent and need fewer participants?

Within-subjects Design(aka Repeated Measures)

Single Sample z-test

Z-tests are very useful calculations when comparing sample and population means to determine if there is a statistically significant difference. After all, the difference between the sample and population means may be due to random chance. These calculations can be used to prove or disprove claims or hypotheses. They require a random sample from a population that is normally distributed and HAS A KNOWN MEAN (average). Z-tests are most useful in large populations, where the sample size is greater than 30.

What are these symbols used for? s SS

s = adjusted standard deviation of sample (s2 = variance) SS = sum of squared deviations [of a set of scores] from their mean

What are some examples of tests used in Inferential Statistics?

t-test Analysis of variance (ANOVA) Chi-Square test

What do these symbols represent? μM σM or SE (standard error)

μM =mean of sampling distribution (of the mean) σM or SE (standard error) = standard deviation of the sampling distribution (of the mean)

Between-Subjects Synonyms

•Between-Ss •Between-group •Independent samples

How do we reduce Variance within groups?

•Hold environmental variables constant. Standardize/automate procedures to be same for everyone (except for IV). •Restrict range of individual variables (e.g., only recruit people age 18-25). [at cost of external validity] •Run more subjects. (larger N is always a good move, when feasible/affordable)

Within-Subjects Synonyms

•Within-Ss •Related samples •Repeated measures •Paired samples •Dependent samples

What do these symbols represent? μ (mu) σ (sigma) σ2

•μ (mu) = mean of population •σ (sigma) = standard deviation of population •σ2 = variance of population