Statistics Final

PSYC 211

What is an independent variable?

the variable being manipulated

What is a dependent variable?

the variable being observed or measured

What are the four scales of measurement?

• nominal

• ordinal

• interval

• ratio

Characteristics of a nominal scale of measurement

• simplest scale

• categorical variables

• does not involve a “rank” of any sort

• can compute only frequency of a level of your variable

  • i.e., there is no meaningful order to the different levels of the variable

  • e.g., favorite color

Characteristics of a ordinal scale of measurement

• involves a rank order of a characteristic

• higher (or lower) values can be considered better than lower values

• can compare between different levels with > or < symbol

• cannot determine by how much one level is different than another

• differences between values do not hold meaning

Characteristics of a interval scale of measurement

• a continuous scale

• differences between values have meaning

• can compare using > or < symbol

• can add and subtract values

  • e.g., fahrenheit

• there is no true zero

Characteristics of a ratio scale of measurement

• a continuous scale in which the differences between values hold meaning and a value of zero holds meaning

• can compare using > or <

• can add and subtract

• can multiply and divide

  • e.g., weight, height, reaction time, age

What should you strive for with scales of measurement?

the most precise measurement

What is reliability?

how consistent (or dependable) a measure is

What is validity?

how accurately a measure captures the construct it is supposed to

A measure cannot be valid if it is not reliable. True or False?

true

As researchers, we strive to observe what?

a participant’s true score

What is an observed score subject to?

measurement error

What are the sources of measurement error?

• transient states (mood)

• stable attributes (motivated to perform well)

• situational factors (gender of researcher, room where test is taken)

• characteristics of the measure (demanding task, ambiguous questions)

• mistakes in recording (how well trained the researcher is, incorrect data)

How can we measure reliability?

• test-retest

• interitem

• interrater

What does a correlation coefficient tell us?

how two measures are related by describing the strength and direction of the relationship

What are the types of validity?

• face validity

• construct validity

  • convergent

  • divergent

A measure cannot be valid if it is not reliable. True or False?

true

What is face validity?

usually assessed by using previous research or asking experts in the field

What is convergent validity?

is our measure correlated with other measures that it should correlate with

What is discriminant validity?

is our measure not correlated with other measures that it should not correlate with

Characteristics of the mean

• describes our typical score, otherwise referred to as the average

• known as the balance point

• changing any single score will change the mean

• introducing a new score or removing a score will change the mean

• adding/subtracting a constant from each score will shift the mean by the constant

• multiplying or dividing each score by a constant will change the mean such that it is multiplied or divided by that constant

How do you calculate the mean?

adding up all values, scores, data points, or observations, then dividing that sum by the number (amount) of observations

How do you weight the mean?

multiple the means by the number of observations in each group

When is a weighted mean usually used?

when individual observations are not provided, but group means are given instead

Characteristics of the median

• the most “center” value in a set of data

• known as the middle point

• changing any single score may or may not change the median

• introducing a new score or removing a score may or may not change the median

• adding/subtracting a constant from each score will shift the median by the constant

• multiplying or dividing each score by a constant will change the median such that it is multiplied or divided by that constant

How do you calculate the median?

• order all values from largest to smallest

• eliminate values from each side until the middle value remains

  • if there is an odd number of scores, the median is the middle score

  • if there is an even number of scores, the median is the average of the two middle scores

What is the mode?

the value that occurs the most frequently

What is a bimodal score?

if there are two values that are the most frequent

What is a multimodal score?

if there are more than two values that are the most frequent

When should you use the mode?

when we have categorical data (nominal scale), we cannot compute the mean or median

When should you use median?

• when we have ordinal data

• when data are skewed

• when outliers are present

• when reporting range and/or inter-quartile range

When should you use mean?

• when we have continuous data (i.e., interval or ratio)

• when data are normally distributed

• there are no outliers

• when reporting variance and/or standard deviation

When should you use mode?

when data are nominal (categorical)

What is variance?

averaged squared deviation from the mean

What is standard deviation?

• averaged deviation from the mean

• by how much individual scores differ from the standard (or mean), on average

• the most commonly reported measure of variability

  • easier to interpret than variance

Why do we use squared deviation scores?

it turns negative deviation scores into positive numbers

What is a z-score?

a way of comparing individuals’ scores to the mean and to other individuals’ scores (i.e., how many standard deviations away from the mean a score is)

What does a z-score indicate?

• how far a score is from the mean

• whether a score is below or above the mean

  • z-scores always have a mean of zero

How can z-scores be helpful for inferential statistics?

can help researchers use the data from a sample to draw inferences about populations

Inferential statistics do what?

makes inferences about a population from a sample

What are the general steps of inferential statistics?

• begin experimental design with a broad topic or theory

• come up with a research question

• make a hypothesis based on related research

  • when we make a hypothesis, we discuss it in terms of conceptual definitions of variables

• operationalize your variables

• run your study; collect data

What is a null hypothesis?

there is no group differences

What is an alternative hypothesis?

there are group differences

When are results statistically significant?

if it is very unlikely that the results were due to chance

When do you reject the null hypothesis?

p < 0.05

we found an effect

↳ difference we observed was not due to chance

When do you fail to reject the null hypothesis?

we did not find an effect

   ↳ difference we observed was due to chance

What is probability?

a portion of all the possible outcomes divided by the total number of possible outcomes

Characteristics of the p-value?

• the probability that an observed difference could have occurred just by random chance

• the larger the p-value, the higher the probability that an effect occurs by chance

• the smaller the p-value, the lower the probability that an effect occurs by chance

  • low p-value indicates statistical significance of the observed differences

What is a Type I error?

reject the null hypothesis when the null is true

What is Type II error?

fail to reject the null hypothesis when the null is false

Characteristics of power

• how well a statistical test can detect an effect

• related to type II error

• probability of rejecting the null hypothesis if the null hypothesis is false

• power of at least .80

  • at least 80% of chance of detecting an effect of the iv

  • 20% of probability of committing a type II error

What is internal validity?

ability to say the iv (and only the iv) causes dv

• concerned with causality

• control for extraneous variables

What is external validity?

generalizability

• concerned with relating to real-world scenarios or with generalizing to other people/places/cultures

What is an observational approach?

direct observation of human and non-human behavior

Characteristics of naturalistic observation

• real-world settings

• no intrusion or intervention by researcher

• participants engage in ordinary activities

• sometimes the researcher will participate in the activities of their subjects in order to better observe

• some drawbacks are losing the ability to judge behavior objectively, or being a part of the group may influence the group

• high external validity

• low internal validity

Characteristics of contrived observation?

• laboratory setting

• participants often know that they are being observed

• controlled environment

• more control over extraneous variables

• less variability in behavior

• high internal validity

• some drawbacks are less generalizability, participants may behave differently because they are being watched, low external validity

What is self-report?

participants or others verbally provide the data

Types of self-reports?

• questionnaires

• interviews

Advantages of questionnaires

• requires less extensive training

• can be administered to groups of individuals

• less expensive and time consuming

• may respond more truthfully to sensitive topics

Advantages of interviews

• follow-up questions allow for more data to be generated

• can be administered to population (e.g., illiterate, children, people who are cognitively impaired, etc) for which questionnaires are inappropriate

• interviewees can ensure that participants understand questions before answering 

Cons to self-reports

• social desirability response bias

  • responding in socially-desirable manner

• acquiescence and nay-saying

  • tendency to agree or disagree with statements

• can overcome social desirability with anonymity and neutrally-worded items

• reverse coding to overcome acquiescence and nay-saying

Types of physiological measurement

• neural electrical activity

• neuroimaging

• autonomic nervous system

• blood and saliva assays

• overt reactions

EEG

• high temporal resolution

• poor spatial resolution

fMRI

• high spatial resolution poorer temporal resolution

Automatic nervous system activity consists of what?

• heart rate

• blood pressure

• respiration

• sweat

• skin temperature

Blood and saliva assays consist of what?

• cortisol

• testosterone

• estradiol

Overt reactions consist of what?

• using specialized equipment to measure subtle bodily reactions

  • sensors to measure blushing

  • pupil dilation

  • eye tracking

What is archival data?

any data that existed before the study

Archival data consists of?

• census data and other government records

• court records

• personal letters

• newspapers and magazines

• social and economic trends

What are the negatives to archival data?

• getting access

• limited to the variables available

• might lack information reliability of measurement

What are probability samples?

• each person in the population has a non-zero chance of being selected, and that probability can be known

• requires access to the full population

• usually not feasible in psychology

What are non-probability samples?

• cannot quantify the likelihood of an individual being selected

• practical

What is simple random sampling?

• equivalent to pulling names out of a hat

• known population

• random selection

• every person in the population has an equal probability of being selected

• requires a sampling frame

What is systematic sampling?

• use when we do not know how many people will participate in the study

• every nth person (e.g., every 3rd, every 5th, etc.)

  • ideal version includes having a sampling frame, picking a random person on the list to start, using that person and every nth person from there

  • less ideal version includes having no sampling frame, using every nth person that becomes available, and not technically random unless you skip a random number of people at the beginning

How to begin stratified random sampling?

• dividing population into strata

  • stratum (singular of strata) - a portion of the population that shares a certain characteristic

    • a homogenous subset of the population

    • requires a sampling frame

Stratified random sampling consists of? 

• randomly sample from each stratum

  • get a specific percentage of your sample from each stratum

  • equally represents each group

• ensure representative percentage from each group

  • could try to match the percentages in the population

    • representative of the population

Descriptive behavior

• cannot determine causality

• only one variable being measured 

Correlational behavior

• discovers the relationship between two variables

• cannot determine causality

• no manipulation of an independent variable

Experimental behavior

• how one variable affects another variable

• manipulation of an independent variable

• random assignments to group

Quasi-experimental behavior

• how one variable affects another when random assignment impossible

• can provide low-moderate support for a causal relationship among variables

• passive manipulation of an independent variable, no random assignment

Correlational analysis

• measures and describes the relationship between two variable

• when conducting a correlation, we are interested in the covariance of two variables

What is covariance?

how do variables change or vary in relation to one another

Positive correlation

two variables tend to change in the same direction

Negative correlation

two variables tend to change in the opposite direction

Correlations can be used to measure?

• validity

• reliability

• prediction

When should you use an independent samples t-test?

• one dichotomous independent variable (two levels)

• one continuous dependent variable (interval or ratio)

• between-subjects design (different participants for each level of the independent variable)

What is the purpose of an independent samples t-test?

• you are determining whether the means of two groups are different than one another

  • does one group systematically differ from the other group?

  • are the two groups from different populations?

  • are the means of two groups significantly different?

What is the critical value of t?

the value of t for which p = .05, or the cutoff t-value

When do you not find significant difference with a t-value?

when the critical t is larger than the t

What is a confounding variable?

a variable other than the iv that differs systematically between conditions

What is the issue with confounding variables?

they invalidate the experiment as it is unclear whether the differences were caused by the iv or the confounding variable, and should be eliminated or restricted as much as possible

What are common types of confounding variables?

• demographic variables (age, gender race, etc.)

• individual differences (reading level, working memory, attention, etc.)

• individual habits (sleep patterns, exercise, diet, etc.)

• external factors (time, weather, etc.)

What are subject variables?

characteristics of the participant (e.g., age, race, hobbies, income sex); otherwise known as individual differences

Are subject variables true independent variables?

no, but they can be treated the same during an analysis

Characteristics of descriptive research

• summarizes and describes behavior

• describes the prevalence of behavior

• cannot determine relationships among variables

Characteristics of between-subjects designs

• each participant experiences only one level of the independent variable

• in order for it to be effective, there must be random assignment

Characteristics of between-subjects designs

• repeated measures design

• all participants experience all levels of the independent variable

What are the advantages to a within-subjects design?

• requires fewer participants

• more statistical power

  • ability to detect the effect of an iv if there is one

• reduces effects of subject variables

What are the disadvantages to a within-subjects design?

• order effects

  • carryover

  • practice

  • sensitization

  • fatigue