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Final Exam Flashcards

1
Q

Where does most of our understanding of the social world come from?

A
  • Authority
  • Tradition
  • Common sense
  • (Social) media
  • Personal experience (experience, observation, interpretation, intuition)
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2
Q

What are sources of bias?

A

Systemic distortions during interpretation.

  • Overgeneralization
  • Selective observation
  • Expectations
  • Premature closure
  • Halo effect
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3
Q

What are the goals of research?

A
  • Description
  • Explanation
  • Prediction
  • Influence
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4
Q

What are the types of research?

A
  • Basic

- Applied

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5
Q

What is basic research?

A

Advances knowledge without necessarily having any obvious practical applications.

  • Description
  • Explanation
  • Prediction
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6
Q

What is applied research?

A

Provides solutions for specific practical problems and advancing quality of life.

  • Influence
  • Solve problem
  • Money
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7
Q

What is science?

A
  • Critical approach to asking questions about how a system works: General methodology independent of subject matter.
  • Process of making structured observation, forming theories, and adapting theories in response to new empirical evidence (data).
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8
Q

What is quantitative research?

A

Systematic empirical study of observable phenomena via statistics and mathematics (describe data using numbers, measurements).

  • Experiments
  • Correlation
  • Surveys
  • Observation
  • Content analysis
  • Existing statistics
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9
Q

What is qualitative research?

A

In depth inquiry into specific experiences by describing and exploring meaning via narrative (describe data using words, images, sounds).

  • Qualitative interviews
  • Focus groups
  • Field research
  • Content analysis
  • Historical-comparitive
  • Alternative production
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10
Q

What is the scientific process?

A
  1. Observation - data collection
  2. Theory - current explanation
  3. Hypothesis - specific prediction
  4. Observation - test prediction
  5. Evaluate/Modify theory
  6. …
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11
Q

What are theories?

A

Integrated systems of assumptions and principles that attempt to organize and predict all currently known observations.

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12
Q

What are the characteristics that scientific theories are evaluated with?

A
  • Falsifiability: Must be testable and rejected (or adjusted) if predictions are not confirmed.
  • Parsimony: Must reflect the simplest possible explanation for the current body of knowledge.
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13
Q

What are hypotheses?

A
  • Testable predictions that are derived logically from theory - falsifiability
  • Describe the specific relationships between two or more variables
  • Acceptance or rejection of allows for evaluation/modification of theories
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14
Q

What are variables?

A

Any characteristic that can have a range of different values (anything that can vary).

  • Data point: individual piece of information
  • Data set: collection/group of data points
  • Data distribution: pattern of the data points
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15
Q

What are descriptive methods?

A

Methods that observe and describe phenomena as they exist and with minimal interference.

  • Naturalistic observation
  • Laboratory observation
  • Case studies
  • Survey research
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16
Q

What is naturalistic observation?

A

Observing behaviour as it occurs in its natural setting and without interference.

  • Natural and spontaneous behaviour
  • Impossible/unethical to manipulate
  • Covert observation of participants
  • Experimenter bias/effects/influence
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17
Q

What is laboratory observation?

A

Observing behaviour without interference in more controlled conditions of the laboratory.

  • Reduction of random variables
  • Allows use of precision equipment
  • Artificial elements become factors
  • Awareness of potential observation
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18
Q

What are case studies?

A

In depth observation of a single or small number of rare or extraordinary cases.

  • Rare phenomena and unique cases
  • Use multiple and varied approaches
  • Gain insight/formulate hypotheses
  • Hard to generalize/draw conclusions
  • Weak basis for normal behaviour
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19
Q

What is survey research?

A

Susceptible to a number of potential weaknesses that may distort results:

  • Sampling bias
  • Wording effects
  • Self-report bias
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20
Q

What is sampling bias?

A

Failure to question/survey sample that is representative of the larger population.

  • Population: group of interest
  • Sample: subset being measured
  • Random/representative sampling
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21
Q

What are wording effects?

A

Subtle changes in wording of a question can lead to dramatically different results.

  • Censorship vs restrictions
  • Welfare vs. aiding the needy
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22
Q

What is self-report bias?

A

Inability to report accurately or honestly on individual’s own behaviours/attitudes.

  • Social desirability
  • Sexual behaviour
  • Racism and sexism
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23
Q

What is correlation?

A

Statistical measure of the strength/direction of the relationship between multiple variables.

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24
Q

What is the correlation coefficient?

A

Numerical representation of the strength and direction of the relationship between variables.

  • Statistical term ‘r’
  • Complete range (-1 to 1)
  • Strength (number 0 to 1)
  • Direction (valence in +/-)
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25
Q

What is positive correlation?

A

Variables increase/decrease together: ranging from 0 (weak) to +1 (perfect).

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26
Q

What is negative correlation?

A

One variables increases/one decreases: ranging from 0 (weak) to -1 (perfect).

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27
Q

What is the experimental method?

A
  • Allows the experimenter to manipulate factors of interest while holding all others constant (controls other factors/influences).
  • Increased control allows the experimenters to determine casual direction: cause and effect.
  • Advantage over all previous methods.
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28
Q

What are experimental variables?

A
  • One variable changes in response to another.

- Dependent changes in response to changes in independent.

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29
Q

What is an independent variable?

A

Represents the specific intervention or the variable that is being manipulated.

  • Varied by the experimenter
  • Multiple treatment/levels
  • Subject/treatment/etc
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30
Q

What is a dependent variable?

A

Outcome of interest that should change in response to the level of the treatment.

  • Any measurable response
  • Stable/reliable/accurate
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31
Q

What are experimental groups?

A

Group of participants that are exposed to the independent variable/treatment.

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32
Q

What are control groups?

A

Group of participants exposed to the same conditions as the experimental group, but not the independent variable.

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33
Q

What criteria does the data require before being adopted?

A
  • Generalizability: apply to other groups
  • Replicability: able to repeat effects
  • Reliability: test yields consistent results
  • Validity: are measuring what you intend
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34
Q

What are the potential issues that might make someone question the validity of experimental findings?

A
  • Confounding and uncontrolled variables
  • Who is studied - sampling/selection
  • Expectation - placebos/blind study
  • Researcher bias - double-blind studies
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35
Q

Why act unethically?

A
  • Publish or perish: career and funding
  • Growing knowledge and certainty
  • Prestige (personal and financial gain)
  • Shortcuts: deadlines, budgets, etc
  • Ignorance, misconceptions, bias, etc
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36
Q

What is scientific misconduct?

A

Violating accepted ethical norms and standards.

  • Research fraud: invent, falsify, distort data or lying about how a study was conducted
  • Misrepresenting findings: p-hacking
  • Plagiarism: presenting another’s ideas, words or work as your own or without proper credit
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37
Q

What are the formal ethics provided by?

A
  • Governments, institutions, professional organizations.
  • Tri-Council Agencies
  • Research Ethics Board
  • Professional code of ethics
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38
Q

What are the ethical guidelines?

A
  • Voluntary/informed consent
  • Freedom to withdraw
  • Protection from harm
  • Confidentiality/anonymity
  • Avoid coercion/deception
  • Debriefing/results
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39
Q

What are levels of measurement?

A

How variables are measured will affect the amount of information you have about them. Level of measurement will influence the types of analysis that we can perform a data set.

  • Nominal
  • Ordinal
  • Interval
  • Ratio
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40
Q

What is nominal?

A

Named categories with no implied hierarchy or ordering among them.

  • Mutually exclusive: only belong to one
  • Collectively exhaustive: all possibilities
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41
Q

What is ordinal?

A

Ordered categories where the distances between them cannot be considered equal. Compare between categories but cannot know the exact difference between them.

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42
Q

What is interval?

A

Equal distances (intervals) between values with an arbitrary zero point. (IQ, rating scales, celsius)

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43
Q

What is ratio?

A

Equal distances between values with a meaningful/absolute zero point. (weight, height, siblings)

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44
Q

What is interval/ratio?

A

Meaningful/absolute zero of ratio variables allows performance of math. Difference between interval and ratio is not an issue for statistical analysis.

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45
Q

What is operationalization?

A

Defining a fuzzy concept to make it distinguishable, measurable and understandable in terms of empirical observations.

  • Define concepts by measurement
  • Attraction/popularity/happiness
  • Nominal/ordinal/interval/ratio
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46
Q

What are descriptive statistics?

A

Present, organize and summarize larger sets of numbers using fewer numbers.

  • Central tendency
  • Variability/spread
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47
Q

What are inferential statistics?

A

Methods that compare groups, or to draw conclusion about population from samples.

  • Statistic (sample)
  • Parameter (population)
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48
Q

What is a population?

A

The entire group that researchers want the results to apply (entire group of interest).

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49
Q

What is a sample?

A

Subgroup being studied.

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50
Q

Why limit research to samples when you are ultimately interested in complete population?

A
  • Population potentially massive
  • Inefficient to study everyone
  • Population changes over time
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51
Q

What are the challenges with using sample over population?

A

Main difficulty is that any sample will differ from the population due to random factors.
- Random error: sample does not equal population
Consequently any difference or association between samples may be due to chance.
- Inferential stats: account for chance

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52
Q

What are representative samples?

A

Minimize random error by collecting data from samples that are representative of populations. This means that the make-up of your sample should approximate that of entire population.

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53
Q

What is a parameter in inferential statistics?

A

Population - summary characteristic of entire population.

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54
Q

What is a statistic in inferential statistics?

A

Sample - summary characteristic of a particular sample from the population.

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55
Q

What is a unit of analysis?

A

Who or what you are measuring - level of unit that provides the data points for your research.

  • Individual
  • Group
  • Company
  • City/county
  • Province/state
  • Country
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56
Q

What are frequency distributions?

A

Summarize distribution of variables by reporting number of responses contained in each category.

  • Variable name/categories of analysis
  • Frequency - number of responses
  • Total number of responses (N)
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57
Q

What is relative frequency?

A

Compares number of responses in specific category to the total number of responses. (proportion) Should add to 1.
rf = f/N

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58
Q

What is percentage?

A

Simple transformation of relative frequency: estimates frequency response/100 cases. Should add to 100.
% = f/N X 100

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59
Q

What is a cumulative frequency?

A

Number of cases with values above/below.

f: 5 19 10
cf: 5 24 34

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60
Q

What is a cumulative percentage?

A

Simple transformation of cumulative frequency: estimates frequency of responses/100 cases.
c% = cf/N X 100

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61
Q

What is grouped frequency?

A

Interval data sometimes spread over larger range of scores making frequency distribution unclear. Condense scores into groups/categories (class intervals) containing more than one score value.

  • Calculate range:highest - lowest
  • Divide range/number of categories
  • Round value up = class interval
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62
Q

What are flexible intervals?

A

Class intervals do not always have to be of the same size: will depend on distribution of data.

  • Expand upper/lower intervals
  • Class intervals of different sizes
  • Relative significance of intervals: depending on variable, differences between intervals can have vastly different meanings (set interval to normalize meaning)
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63
Q

What is a proportion?

A

p = f/N

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64
Q

What is a percentage?

A

% = f/N X 100

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65
Q

What is a ratio?

A

f1/f2 X Base

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66
Q

What is a cross-tabulation?

A

Table that presents distribution of one variable (usually dependent) across categories of one or more variables (usually independent).

Can express the frequencies of each cell as percentages:

  • Column totals
  • Row totals
  • Sample total
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67
Q

What are measures of central tendency?

A

Express groups of scores in terms of their middle most value. Effectively summarize groups of scores and facilitate individual and group comparisons.

  • Mean
  • Median
  • Mode
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68
Q

What is the mean?

A

Arithmetic mean is the primary index of central tendency for interval and ratio data. Allows for the comparison of groups of different sizes- score value per subject.
mean = sum of all scores/number of scores
X(bar) = ∑X/n

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69
Q

What is the mean formula for a population?

A 
u = ∑Xi/N
u: mean of population (mu)
∑: stigma - sum of
Xi: particular score/observation
N: number of scores (population)
X: individual score/observation
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70
Q

What is the mean formula for a sample?

A 
X(bar) = ∑Xi/n
X(bar): mean of sample
∑: stigma - sum of
Xi: particular score/observation
n: number of scores (sample)
X: individual score/observation
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71
Q

What are the deviation scores?

A

Total distance of all scores above the mean equals the total distance of all scores below the mean (sum always zero).
Subtract each point from the mean, add them all to get 0.

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72
Q

What are outliers?

A

Extreme values that pull the mean away from the central tendency of distribution.

73
Q

What is the median?

A

Value where half of all scores fall above and half fall below - rank order scores and count to the middle value.
- Odd: count to middle most value
- Even: Average of both middle values
median = N+1/2 (not the median but where the median is placed)

74
Q

How does the median help?

A

Inappropriate for most inferential statistics, sometimes better for descriptive statistics.

  • Minimzes extreme scores
  • Floor and ceiling effects
  • Only option for ordinal data
75
Q

What is the mode?

A

Most frequently occurring score in distribution.

  • Only option for nominal
  • Unimodal (one mode - one bump)
  • Bimodal (two modes - two bumps)
  • Multimodal (many modes)
76
Q

What is the normal distribution?

A

Theoretical bell-shaped frequency distribution that is unimodal and symmetrical: approximated in nature and research.

  • Mean = median = mode
  • Symmetric/zero skew
  • Mosokurtic
  • Asymptotic tails (doesn’t touch x-axis)
77
Q

What is skewness?

A

Refers to the symmetry, or lack of symmetry, of the distribution.

  • Positive = tail skewed right (flat part of curve on right)
  • Negative = tail skewed left
78
Q

What is kurtosis?

A

Refers to how flat or curved the shape of the distribution is.

  • Leptokurtic: peaked (low variability)
  • Mesokurtic: normal
  • Platykurtic: flat (high variability)
79
Q

What is the five-number summary?

A

Descriptive statistics that provide information about dataset - five most important percentiles.

  • Sample minimum: 0% below/100% above (lowest point)
  • First/lower quartile: 25% below/75% above (median of the lower half)
  • Median sample: 50% below/50% above (median)
  • Third/upper quartile: 75% below/25% above (median of the upper half)
  • Sample maximum: 100% below/0% above (highest point)
80
Q

What are pie charts?

A

Circular chart using slices to represent frequencies or percentages - all slices add up to 100%.

  • Nominal variables only (ordinal possible/weird)
  • Explode slice of interest (one slice pokes out more)
  • Approximately five categories
81
Q

What are graphs?

A

Represent data as a series of bars of different lengths: unlimited variables and all levels of measurement. Bars generally (not always) arranged so category is along x-axis and value is along y-axis.

  • Bar graph
  • Histogram
82
Q

What is a bar graph?

A

Space out bars to represent discontinuity between (nominal) variables.

83
Q

What is a histogram?

A

Bars touch to represent continuity between (interval) variables.

84
Q

What are frequency polygons?

A

Plot frequencies or midpoints of intervals then connect the dots.

  • Ordinal/interval data since it highlights continuity
  • Connect lines to estimate values
85
Q

What are measures of variability?

A

Express the pattern or spread of individual scores around the mean.

  • Pattern of scores around the mean
  • Distance of scores from other scores
86
Q

What is the range?

A
  • Difference between the highest and lowest scores in a distribution - simplest measure.
  • Expressed as interval containing all scores in the distribution from lowest to highest.
87
Q

What are deviations from the mean?

A

Distance (deviation) of individual scores in a distribution from the mean of the distribution.
deviation score = Xi - X(bar)
∑(Xi - X(bar)) = 0 always

88
Q

What is the mean deviation?

A

Average deviation of a score from the mean: average absolute values of difference scores.
mean deviation = ∑|Xi - X(bar)| / n
- Would be great measure of variability, except for absolute values

89
Q

What is variance?

A

Average of the squared deviations from the mean - spread of scores around the mean. Square the deviation scores instead of using absolute values - solves problem.

  • Sum of squares (SS) ∑ (Xi - X(bar))^2
  • Divide by N or n-1

Does reasonable job representing variability in the data but expressed in units squared. Squaring results in large values makes relating to mean difficult.

90
Q

What is the formula for variance in population?

A

o^2 = ∑(X-u)^2 / N

91
Q

What is the formula for variance in sample?

A

s^2 = ∑(X - X(bar))^2 / n-1

Divide by n-1 because sample variance underestimates population variance.

92
Q

What is standard deviation?

A

Calculated by taking the square root of the variance - average variability around mean. Comparison easy, same units as mean.

93
Q

What are Z scores?

A

Number of standard deviations that a particular score is away from the mean of its distribution. Using standard deviation as the unit of reference allows for immediate understanding of where the score fits into the distribution.

  • Compare scores on different distributions
  • Percent of scores above/below the score
  • Exact placement of the normal distribution
94
Q

How to calculate z scores (raw score to z score)?

A
  1. Calculate deviation score
  2. Divide by standard deviation
    Z = X-X(bar) / s
    - Negative: below mean
    - Positive: above mean
95
Q

How to calculate raw score (z score to raw score)?

A
  1. Multiply Z score by standard deviation
  2. Add deviation score to the mean
    X = X(bar) + (Z)(SD)
96
Q

What is standard normal distribution?

A

Shape of the distribution of standard scores will always match distribution of raw scores.

  • Mean of Z scores = 0
  • Standard deviation = 1
  • Area under curve = 1
97
Q

What are standard scores?

A

Converting to Z scores allows you to compare scores that come from different distributions.

  • Different means/standard deviations
  • Normalizes to 0/1
98
Q

What does knowing the Z score allow you to determine?

A
  • Percentage of scores above/below that score
  • Percentage of scores between any two scores
  • Z score value for any particular percentage
99
Q

What is probability?

A

Relative likelihood that one particular outcome will or will not occur relative to some other outcome.
- Outcome: result unknown in advance
- Frequency: times something happens
Expected relative frequency
probability = successful outcomes / all possible outcomes

100
Q

What is the range of probability?

A

Proportion of possible successful outcomes to the total number of possible outcomes: never less than 0 or greater than 1.

  • p = 1: absolute certainty (100%)
  • p = 0: complete impossibility (0%)
101
Q

What is the probability addition rule?

A

Probability of mutually exclusive events occurring is sum of individual probabilities. Mutually exclusive means that one outcome excludes the possibility of all others occurring.
- Sum of all outcomes: p = 1

102
Q

What is the probability multiplication rule?

A

Probability of multiple independent outcomes occurring is product of individual probabilities. Independent outcomes mean that the outcome of one event has no influence on another event.

103
Q

What is the gambler’s fallacy?

A

Belief that if/when deviations from expected results are observed, future deviations in the opposite direction are more likely.

  • Repeated losses does not mean you are due to win
  • Outcome independent of previous outcomes
  • Probabilities even out only after infinite trials
104
Q

What does probability have to d with everything else?

A

Any distribution can be defined in terms of its mean and standard deviation.

  1. Assume normal distribution
  2. Normalize data - convert to Z
  3. Exact probability of any score
105
Q

What is probability?

A

Relative likelihood that one particular outcome will (or will not) occur relative to some other outcomes.

106
Q

p=1 means?

A

Absolute certainty (100%)

107
Q

p=0 means?

A

Complete impossibility (0%)

108
Q

p>0 means?

A

Reflects a possible outcome: unlikely/improbable not impossible.

109
Q

What is the addition rule?

A
  • The or rule
  • Add the possibilities
  • Sum of all outcomes: p=1
110
Q

What is the multiplication rule?

A
  • The and rule

- Multiply the possibilities

111
Q

What is the normal distribution?

A
  • Mean = median = mode
  • Symmetric/zero skew
  • Mesokurtic
  • Asymptotic tails
112
Q

What are Z scores?

A
  • Number of standard deviations that a particular score is away from the mean of its distribution.

Z = (X-Xbar)/SD

113
Q

How do you calculate the raw score?

A

X = Xbar + (Z)(SD)

114
Q

What does converting to Z scores allow?

A

Allows you to compare scores that come from different distributions.

115
Q

How do you calculate what percentage/area is above a certain score?

A
  • Calculate the Z score
  • Find the proportion that matches the Z score in the Z table
  • Subtract this value from 0.5 or 50%
116
Q

How do you calculate what percentage/area is below a certain score?

A
  • Calculate the Z score
  • Find the proportion that matches the Z score in the Z table
  • Subtract this value from 0.5 or 50%
117
Q

How do you calculate what percentage/area is between two scores?

A
  • Calculate the Z score of each
  • Find the proportion that matches the Z scores in the Z table
  • Add both of these values
118
Q

How do you calculate what percentage/area is outside (above and below) two scores?

A
  • Calculate the Z score of each
  • Find the proportion that matches the Z scores in the Z table
  • Add both of these values
  • This will be the value between so then subtract it from 1 or 100% (evenly split on both sides of the curve)
119
Q

How do you calculate what score is within a certain percentage?

A
  • Find the proportion in the Z table and its corresponding Z score
  • Use the raw score formula
120
Q

How do you calculate what score is within the middle 50%?

A
  • Find the proportion in the Z table and its corresponding Z score
  • Use the raw score formula twice (one for positive Z and one for negative)
121
Q

What is a population?

A

Entire group of interest.

122
Q

What is a sample?

A

Subgroup being studied.

123
Q

Why limit research to samples when you are ultimately interested in complete population?

A
  • Population potentially massive
  • Inefficient to study everyone
  • Population changes over time
124
Q

What is the challenge to limiting research to samples?

A

Main difficulty is that any sample will differ from the population due to random factors. (sampling error)

125
Q

What do inferential stats do?

A

Accounts for chance.

126
Q

What is sampling error?

A

Difference between a sample statistic and a population parameter due to random factors and/or sampling.

127
Q

What is random sampling?

A

A technique where all units in population have equal and non-zero chance of being included in the sample:

  • Equal probability of inclusion
  • Selection of units independent
  • Any/all combinations possible
128
Q

What is sampling distribution of means?

A
  • One way to estimate sampling error is by calculating this - inefficient and only modeled theoretically.
  • It is calculated from multiple random samples drawn from same population:
    Mean of means - population mean
    Standard deviation - sampling error
129
Q

What are the three simple rules that allow us to determine the basic characteristic of sampling distribution of the means?

A
  • Distribuation mean = population mean
  • Standard deviation less than population
  • Distribution approximately normal
130
Q

What is distribution mean = population mean?

A

Mean of sampling distribution of the means calculated from means of an infinite number of smaller samples from the population.

  • Distributed around population mean
  • Reduces impact of extreme scores
131
Q

What is standard deviation less than population?

A

Distribution is made up from the means of infinite samples -> Extreme scores become less likely.

  • Averaging candles extreme scores
  • Results in more regular distribution
132
Q

What is distribution approximately normal?

A

Regardless of distribution of original scores, the sampling distribution of the mean tends to be normally distributed.

  • Extreme scores wash out
  • Sample size is normal
133
Q

What is the central limit theorem?

A

If repeated random samples of size n are taken from a population with the mean u and standard deviation o, then the sampling distribution of the mean;

  1. Mean equal to population mean (u)
  2. Standard error equal to (oXbar = o/sqrt*n)
  3. Approach normal as n increases
134
Q

What is the formula for the standard error of a population?

A

oXbar = o / sqrt*n

135
Q

What is the formula for the standard error of a sample?

A

sXbar = s / sqrt*n

136
Q

What does standard deviation do?

A

Standard deviation estimates the distance of any score from the sample/population mean.

137
Q

What does the standard error do?

A

Standard error estimates the distance of any sample mean from the population mean.

138
Q

What are confidence intervals?

A
  • Confidence intervals estimate the range of possible means that are likely include the population mean.
  • Usually intervals of 95% or 99% confidence
139
Q
  • Confidence intervals estimate the range of possible means that are likely include the population mean.
  • Usually intervals of 95% or 99% confidence
A
  • Calculate standard error
  • Use Z score of +- 1.96 for 95% and +- 2.58 for 99%
  • CI = Xbar +- (z)(oXbar)
  • Write answer as # - #
140
Q

How do we calculate confidence intervals when sample standard deviation(s) is known?

A
  • Calculate standard error
  • Calculate n-1 for degrees of freedom (df)
  • Use level of significance of 0.05 for 95% and 0.01 for 99%
  • Use df and level of significance to find t statistic in t distribution table
  • CI = Xbar +- (t)(sXbar)
  • Write answer as # - #
141
Q

What is the interpretation of the confidence intervals?

A

Confidence interval establishes certainty that mean falls within the interval - NOT certainty that sample mean equals population mean.

  • Not exact estimate
  • Might be incorrect
  • Probably correct
142
Q

What is the formula for the standard error of the proportion (sp)?

A

sp = sqrt of ( (P(1-P)) / n )

143
Q

How do we calculate confidence intervals with the standard error of proportion?

A
  • Calculate standard error
  • Use Z score of +- 1.96 for 95% and +- 2.58 for 99%
  • CI = P +- (z)sp)
  • Write answer as # - #
144
Q

What is the margin of error?

A

margin of error = (z)(sp)

145
Q

What are descriptive statistics?

A

Present, organize and summarize larger sets of numbers using fewer numbers.
- Central tendency and variability

146
Q

What are inferential statistics?

A

Analyses that compare groups or draw conclusion from samples and populations.
- Z and t test

147
Q

What is hypothesis testing?

A
  • Method of statistical inference comparing sampled data to other sampled data, theoretically modeled data, or population parameters.
  • Method purposes alternate hypotheses describing predicted relationships between variables of study.
148
Q

What is the null hypothesis (H0)?

A
  • Default position is that there is no relationship between variables / association among groups.
  • Assume groups are equivalent
  • There is no difference between …
149
Q

What is the alternate hypothesis (H1)

A
  • Describes the predicted relationship between variables that you are currently investigating.
  • Assumes that some difference exists
  • There is a difference between …
150
Q

What is the level of significance (a)?

A
  • Researches determine what represents a real difference between means in advance.
  • Typically a = 0.05 or 0.01 (convention)
  • Translates to there being less than 5% or 1% probability of the result occurring by chance.
151
Q

What is the critical value?

A

Value that the calculated test statistic (result) must meet or exceed to consider the difference real.

  • Depends on level of significance
  • Depends on the distribution used (Z or t)
152
Q

What is the formula for the Z test of the test statistic?

A

Z = (Xbar - u) / oXbar

153
Q

What critical values are used for the Z test?

A

For a = 0.05, it is +- 1.96

For a = 0.01, it is +- 2.58

154
Q

What do we do when test statistic (Z or t) exceeds critical value?

A

Test statistic (?) exceeds critical value, reject null hypothesis. Conclude that difference is probably real at (0.05 or 0.01) significance.

155
Q

What do we do when test statistic (Z or t) does not exceed critical value?

A

Test statistic (?) does not exceed critical value, retain null hypothesis. Conclude that there is no difference at (0.05 or 0.01) significance.

156
Q

What is the formula for the t test of the test statistic?

A

t = (Xbar - u) / sXbar

157
Q

What critical values are used for the t test?

A

Use t table to find df (n-1) for a = 0.05 and a = 0.01.

158
Q

What are directional hypotheses?

A
  • All out previous analyses comparing means test to see if means differ in either direction - two-tailed test
  • We can also perform analyses to specifically test if one mean is higher or lower - one-tailed test
    Hypothesis not only predicts a difference, but also predicts the specific direction of the difference
159
Q

What is a two-tailed test?

A
  • Predicts the results will differ - but down not suggest the direction
  • Equal sensitivity at both ends
160
Q

What is a one-tailed test?

A
  • Predicts the results will differ - that they will be higher/lower
  • Greater sensitivity at one end
  • Test becomes more likely to discover a difference
161
Q

How to calculate Z test with two-tailed?

A

Z 0.05 = +- 1.96

Z 0.01 = +- 2.58

162
Q

How to calculate Z test with one-tailed?

A

Z 0.05 = 1.65

Z 0.01 = 2.33

163
Q

How to calculate t test with two/one-tailed?

A

They have separate tables.

164
Q

What are decision errors?

A
  • Situations where right procedure leads to wrong conclusions regarding rejecting or retaining null hypothesis.
  • Drawing conclusions about population using information drawn from samples involves risk.
165
Q

What is a Type I Error (a)?

A

Rejecting null hypothesis when it is actually true - significant result when no difference exists (false positive).

  • Probability: a = p(0.05 or 0.01)
  • Smaller p value reduces risk
166
Q

What is a Type II Error (B)?

A

Retaining the null hypothesis when alternate hypothesis is true - non-significant result when difference exists.

  • Probability: B(multiple factors)
  • Smaller p value increases risk
167
Q

What does reducing p value do to each error?

A

Reducing p value decreases risk of Type I Error while increasing risk of Type II Error

168
Q

How do you control Type I Error?

A

To decrease type I is to arbitrarily lower the p value.

  • Increases Type II Error
  • Violation of Conventiom
169
Q

How do you control Type II Error?

A

Arbitrarily increasing the p value is not feasible - other steps used to decrease Type II Error

  • Increse sample size
  • Incease treatment effects
  • Decrease experimental error
170
Q

What are single sample tests?

A
  • These tests allow us to deterine if a sample is likely to have been drawn from a population.
  • Calculate test statistic from difference of means: compare it to the critical value (Z/t)
171
Q

What are two sample tests?

A
  • Used to examine if sample means differ from each other, instead of if it differs from the population mean.
  • Related and Independent samples t tests
172
Q

What are related samples t tests?

A
  • Compare means of related samples: samples that were not chosen independently from each other (scores dependent on each other)
  • Usually same group of people that are tested twice (before/after, two halves of a pair…)
  • Both samples always of equal sizes
173
Q

How do we calculate the degrees of freedom for the related samples t tests?

A

n-1

174
Q

What are the formulas for the related samples t tests (never used in class before)?

A
  • Difference of scores (d): simple difference between pairs of scores
  • Mean of the differences: Dbar = sum of d / n
  • Standard deviation of the differences: sd = sqrt of (sum of (d-Dbar)^2 / (n-1) )
  • Standard error of the mean difference: sDbar = sd/sqrt*n
  • t test: t = Dbar / sDbar
175
Q

What are the interpretations to the related samples t tests?

A
  • Reject H0 if t value > critical value

- Retain H0 if t value < critical value

176
Q

What are independent samples t tests?

A
  • Compare means of independent samples: samples that were chosen independently from each other.
  • Any comparison between samples where selection of each sample occurs independently of the other.
  • Samples of random composition and not matched in any way
  • Can be same or different sizes
177
Q

How do we calculate the degrees of freedom for the independent samples t tests?

A

n1 + n2 - 2

178
Q

What are the formulas for the related independent samples t tests (never used in class before)?

A
  • Means and standard deviations: calculate mean andSD of each sample separately
  • Estimate population variance: s^2 = [ s1^2 (n1-1) + s2^2 (n2-1) ] / (n1 + n2 -2)
  • Standard error of the difference of means: sXbar1 - Xbar2 = sqrt of [ s^2 ( (n1+n2) / (n1n2) ) ]
  • t test: t = (Xbar1 - Xbar2) / (sXbar1 - Xbar2)
179
Q

What are the interpretations to the independent samples t tests?

A
  • Reject H0 if t value > critical value

- Retain H0 if t value < critical value

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