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QM > Test 2 > Flashcards

Test 2 Flashcards

1
Q

What is probability?

A

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

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2
Q

p=1 means?

A

Absolute certainty (100%)

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3
Q

p=0 means?

A

Complete impossibility (0%)

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4
Q

p>0 means?

A

Reflects a possible outcome: unlikely/improbable not impossible.

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5
Q

What is the addition rule?

A
  • The or rule
  • Add the possibilities
  • Sum of all outcomes: p=1
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6
Q

What is the multiplication rule?

A
  • The and rule

- Multiply the possibilities

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7
Q

What is the normal distribution?

A
  • Mean = median = mode
  • Symmetric/zero skew
  • Mesokurtic
  • Asymptotic tails
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8
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

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9
Q

How do you calculate the raw score?

A

X = Xbar + (Z)(SD)

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10
Q

What does converting to Z scores allow?

A

Allows you to compare scores that come from different distributions.

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11
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%
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12
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%
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13
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
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14
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)
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15
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
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16
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)
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17
Q

What is a population?

A

Entire group of interest.

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18
Q

What is a sample?

A

Subgroup being studied.

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19
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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20
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)

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21
Q

What do inferential stats do?

A

Accounts for chance.

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22
Q

What is sampling error?

A

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

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23
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
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24
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
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25
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
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26
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
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27
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
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28
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
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29
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
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30
Q

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

A

oXbar = o / sqrt*n

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31
Q

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

A

sXbar = s / sqrt*n

32
Q

What does standard deviation do?

A

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

33
Q

What does the standard error do?

A

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

34
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
35
Q

How do we calculate confidence intervals when population standard deviation(o) is known?

A
  • Calculate standard error
  • Use Z score of +- 1.96 for 95% and +- 2.58 for 99%
  • CI = Xbar +- (z)(oXbar)
  • Write answer as # - #
36
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 # - #
37
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
38
Q

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

A

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

39
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 # - #
40
Q

What is the margin of error?

A

margin of error = (z)(sp)

41
Q

What are descriptive statistics?

A

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

42
Q

What are inferential statistics?

A

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

43
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.
44
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 …
45
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 …
46
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.
47
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)
48
Q

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

A

Z = (Xbar - u) / oXbar

49
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

50
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.

51
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.

52
Q

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

A

t = (Xbar - u) / sXbar

53
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.

54
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
55
Q

What is a two-tailed test?

A
  • Predicts the results will differ - but down not suggest the direction
  • Equal sensitivity at both ends
56
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
57
Q

How to calculate Z test with two-tailed?

A

Z 0.05 = +- 1.96

Z 0.01 = +- 2.58

58
Q

How to calculate Z test with one-tailed?

A

Z 0.05 = 1.65

Z 0.01 = 2.33

59
Q

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

A

They have separate tables.

60
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.
61
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
62
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
63
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

64
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
65
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
66
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)
67
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
68
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
69
Q

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

A

n-1

70
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
71
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

72
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
73
Q

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

A

n1 + n2 - 2

74
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)
75
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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