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Intro Stats at UMass Lowell > skills > Flashcards

skills Flashcards

1
Q

01 rate versus percent

A

Rate is per capita, and used to analyze groups of different size. It is per person versus per one hundred people. You divide the number of observations by the total number in the population.

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2
Q

1 how to identify the individuals and variables in a dataset

A
  • Individuals are the objects described by a set of data. Individuals may be people, but they may also be animals or things.
  • A variable is any characteristic of an individual. A variable can take different values for different individuals.
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3
Q

1 how to identify categorical VS quantitative variables (and the units of measurement for each quant. var.)

A

quants are numbers that can be measured, categories can contain words and choices

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4
Q

1 • SPSS • how to make a pie chart

A

SPSS

  1. Graphs → Chart Builder
  2. Gallery → Pie/Polar; Pie Chart → Chart Preview
  3. drag to determine “slice by” and “angle variable” in chart preview
  4. In Element Properties, under Statistics, “Statistic:” select “value”
  5. (Apply if necessary)
  6. Done
  7. Double click to edit in Chart Editor
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5
Q

1 how to recognize when a pie chart can and cannot be used

A

A pie chart must include all the categories that make up a whole. Use a pie chart only when you want to emphasize each category’s relation to the whole.

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6
Q

1 • SPSS • how to make a bar graph of a cat. var. dist.

A

SPSS

  1. Graphs → Chart Builder
  2. Gallery → Bar; Bar Chart → Chart Preview
  3. Drag to axes
  4. Element Properties → Statistics → Statistic → Value
  5. double click to open chart editor
  6. Properties → Categories
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7
Q

1 • SPSS • how to make a histogram of a quant. var. dist.

A
  1. Variable view
  2. Analyze –> Descriptive Statistics –> Frequencies
  3. Move desired variable to “Variables” –> click CHARTS
  4. Under chart type, select histogram
  5. optional: select show normal curve
  6. Continue –> OK
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8
Q

1 How to describe skewness

A
  • A distribution is skewed to the right if the right side of the histogram(containing the half of the observations with larger values) extends much farther out than the left side.
  • It is skewed to the left if the left side of the histogram extends much farther out than the right side.
  • the mean moves towards the skew. a larger mean is right skewed and positive, and vice versa.
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9
Q

1 how to describe a histogram

A

shape, center and variability or spread. roughly symmetric, distinctly skewed or neither. Existence of outliers.

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10
Q

1 •SPSS • how to make and assess a stem plot,
incl. round leaves and split stems

A

MAKE

  1. Analyze –> descriptive statistics –> explore
  2. move variable to dependent list –> click plots
  3. Select “Stem and leaf” under descriptive –> continue –> OK

ASSESS

  • how many peaks does it have?
  • if a long tail goes (down) toward the larger numbers it is “right-skewed”
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11
Q

1 • SPSS • how to make a time plot, and recognize trends and cycles

A

SPSS

  1. Graphs –> Chart Builder
  2. Gallery: select scatter/dot
  3. Then drag simple scatter to chart preview section
  4. define axes by dragging (time unit goes to X)
  5. THEN ADD INTERPOLATION LINE
  6. click button in attachment in chart editor
  7. select straight from line type
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12
Q

2 • SPSS • how to find the mean x̄ and standard deviation s for a set of observations

A

MANUAL

basically the average

SPSS

  1. Analyze –> descriptive statistics –> frequencies
  2. moved desired variable to “variables,” –> click “statistics”
  3. Under percent values, click quartiles, and all other checkboxes needed
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13
Q

2 how to find the Median M and quartiles Q1 and Q3 for a set of observations

A

To find the median

  1. arrange all observations in order of size from smallest to largest
  2. if the number of obs. is ODD, the M is the center obs.
  3. if the n is EVEN, the M is midway btw the two center obs
  4. or use (n+1)/2 <– note: this just gives the location of the median
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14
Q

2 know whether the mean or the median are resistant, and know what skewness does

A

the median is more resistant that the mean, and skewness moves the mean away from the median toward the long tail

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15
Q

2 how to assess a box plot

A
  • look at center, spread, symmetry and skewness
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16
Q

2 • SPSS • how to find the five number summary and draw a box plot

A

to find the five number summary

  1. list the lowest and highest observation, the median, and then the medians of each half

To make a box plot in SPSS

  1. Variable view
  2. Analyze –> Descriptive Statistics –> Explore
  3. Move variable to dependent list, click plots
  4. Under Boxplots –> Factor levels together
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17
Q

2 know how to find the variance and standard deviation

A
  • the standard deviation and variance measure the variability by looking at how far the observations are from their mean
  • find the variance by averaging the squares of the difference between each observation and the mean and then dividing by the number of observations minus one
  • the standard deviation is the square root of the variance
  • you divide by n-1 because the deviations always sum to 0 and you need to not be dividing by zero (kind of)
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18
Q

2 know the basic properties of standard deviation

A
  • s ≥ 0 always
  • s = 0 only when all observations are identical and increases as the spread increases
  • s has the same units as the original measurements
  • s is pulled strongly by outliers and skewness
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19
Q

3 how to approximately locate the mean and median on a density curve

A
  • the median is the equal areas point
  • the mean is the balance point
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20
Q

3 how to use the 68-95-99.7 rule and symmetry to state what percent of observations of a normal distribution fall between two points.

A
  • The mean and standard deviation will be listed as N(?,?)
  • 68% will fall within one standard deviation σ
  • 95% will fall within 2σ
  • 99.7% will fall within 3σ
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21
Q

3 how to find the z-score or “standardized value,” and what it means for a normal distribution

A

The z-score, or standardized value, tells us how many standard deviations the original observation falls away from the mean, and in which direction.

to find it you subtract the mean of the distribution from X and then divide by the standard deviation, as attached.

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22
Q

3 how to calculate the proportion of values above, below or between certain numbers when given a stated mean μ and standard deviation σ

A
  1. state the problem and draw a picture
  2. use Table A backward. Find the given proportion in the body of the table and then read the corresponding z from the left column and top row.
  3. unstandardize z back to X… x lies the z amount standard deviations away from the mean, so : x = (the mean) plus (the standard deviation) times (the z-score that we are given)
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23
Q

3 • SPSS • how to determine area to the left in a normal distribution (i.e. probability a score will fall within a certain range)

A

SPSS

  1. new data set, variable view
  2. create variable “[variable]” you want to see what is to the left of
  3. data view, enter desired area to the left (e.g. 0.95 for 95th%)
  4. Transform –> compute variable
  5. Target variable: Prob
  6. Function Group: CDF & Noncentral CDF
  7. Functions and Special variables: Cdf.Normal
  8. CDF.NORMAL(?,?,?) <– first ? =”[variable]”, Mean and SD
  9. Click OK
  10. You get a two decimal amount, click to see more decimals
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24
Q

3 • SPSS • how to determine percentiles for normal distributions

A

SPSS

  1. new data set, variable view
  2. create variable “area”
  3. data view, enter desired area to the left (e.g. 0.95 for 95th%)
  4. Transform –> compute variable
  5. Target variable: “percentile”
  6. Put cursor in Numeric Expression then Function Group menu select “Inverse DF”
  7. From Functions and special variables menu, double -click “Idf.Normal”
  8. “IDF.NORMAL(?,?,?)” will appear in Numeric Expression box
  9. select first question mark and place the variable “area” there
  10. Replace second question mark with Mean
  11. Replace third question mark with standard deviation
  12. Click OK
  13. Data editor will now display percentile
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25
Q

3 how to use the standard normal table

A
  1. draw a picture of the distribution (any area to the right ( x ≥ ? ) are 1-area to the left)
  2. Standardize. The proportion minus mean mu divided by standard deviation sigma = a number
  3. find that number on the table BUT if it’s an x ≥ problem, then subtract that number from 1.
  4. to find sections, repeat above and do the math converting x to z or see 3.7
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26
Q

3 how to calculate the point having a stated proportion of all values above it or below it, when given a stated mean µ and standard deviation σ

A
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27
Q

4 how to identiify explanatory VS response variables

A
  • A response variable measures an outcome of a study. An explanatory variable may explain or influence changes in a response variable.
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28
Q

4 • SPSS • how to make a scatterplot to display the relationship between two quant. variables and know which scale to put the explanatory variable on.

A

SPSS

  1. Analyze → Correlate → Bivariate
  2. move variables into window
  3. Graphs → Legacy Dialog → Scatter/Dot
  4. Simple Scatter → Define
  5. put explanatory on X, response on Y, OK
  6. Elements → Fit Line at Total
  7. Analyze → Regression → Linear
  8. put explanatory in independent, response in dependent, OK
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29
Q

4 how to describe a scatterplot

A

you describe its direction, form and strength, positive or negative association and outliers

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30
Q

4 how to add a categorical variable to a scatterplot by using a different plotting symbol or color

A

when making the scatterplot, after you determine the axes, move a categorical variable into the “set markers by” box, go into chart editor and select the little legend symbols to edit shape and color

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31
Q

4 • SPSS • how to find the correlation r

A

correlation measures the strength and direction of the linear relationship

SPSS: look at regression cards

  • The values for each individual are x1 and x2, y1 and y2, etc
  • the mean is x̄ (or y-bar)
  • the standard deviation is sx and sy
  • so correlation is (([the first x individual value] minus [x’s mean] divided by [x’s standard deviation]) + the next and next etc) divided by x’s standard deviation, then also for y, added all up ALL divided by the number of individuals n-1
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32
Q

4 how to judge whether it’s appropriate to use correlation to describe the relationship between two variables

A
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33
Q

5 how to draw a graph of a regression line when you are given its equation

A
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34
Q

5 • SPSS • how to use the regression line to predict y for a given x, and also recognize extrapolation

A
  1. Analyze –> regression –> Linear
  2. Response variable –> dependent, explanatory –> independent
  3. save… Predicted values “Unstandardized”
  4. Click OK for basic linear regression output
  5. “Model Summary” (2nd table): R = absolute value of small r… R Square = the square thereof and stanard error
  6. Coefficients (4th (bottom) table) “1 (Constant)” at “B” is the Y intercept
  7. “[Explanatory variable] at “B” is the slope
  8. back to dataset see a new column of predicted values based on slope
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35
Q

5 • SPSS • how to explain what the slope b and the intercept a mean in the equation

ŷ=a +bx

A

Use SPSS to calculate (resression cards has it)

  • b is the slope, i.e. the amount by which Y changes when X increases by 1
  • a is the y-intercept, the value of Y when X = 0
  • find the slope and intercept attached
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36
Q

5 how to use a calculator to find the least squares regression line of a response variable y on an explanatory variable x

A
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37
Q

5 • SPSS • how to find the slope and the intercept of the least squares regression line from the means and standard deviations of x and y and their correlation

A
  1. Analyze –> regression –> Linear
  2. Response variable –> dependent, explanatory –> independent
  3. Click OK for basic linear regression output
  4. “Model Summary” (2nd table): R = absolute value of small r… R Square = the square thereof and stanard error
  5. Coefficients (4th (bottom) table) “1 (Constant)” at “B” is the Y intercept
  6. “[Explanatory variable] at “B” is the slope
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38
Q

5 • SPSS • how to calculate the residuals and plot them against the explanatory variable x.

A
  1. Analyze –> regression –> Linear
  2. Response variable –> dependent, explanatory –> independent
  3. save… –> unstandardized
  4. Click OK for basic linear regression output
  5. “Model Summary” (2nd table): R = absolute value of small r… R Square = the square thereof and stanard error
  6. Coefficients (4th (bottom) table) “1 (Constant)” at “B” is the Y intercept
  7. “[Explanatory variable] at “B” is the slope
  8. back to dataset a new variable has been added
  9. graph –> legacy dialogue –> scatter
  10. Simple –> explanatory on the X, new residuals on the Y
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39
Q

5 how to use r<em>2</em> the square of the correlation, to describe how much of the variation in one variable can be accounted for by a straight line relationship with another variable

A
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40
Q

5 recognize lurking variables

A

a variable that is not included as an explanatory or responsevariable in the analysis but can affect the interpretation of relationships betweenvariables

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41
Q

8 how to identify the population in a sampling situation

A
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42
Q

8 how to recognize bias

A

often due to voluntary response and other inferior sampling methods

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43
Q

8 recognize the presence of undercoverage and non-response, as well as poor wording, in a sample survey

A
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44
Q

8 • SPSS • how to use software or table B of random digits to select an SRS from a population

A

SPSS

  1. Data –> Select Cases
  2. select “Random Sample of cases. click Sample
  3. decide whether you want a percentage of fixed number of cases, continue
  4. Decide on “output”
  5. makes a filter variable column with zeroes for filtered or 1’s
  6. go to variable view and rename filter to variable 1 or whatever
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45
Q

8 • SPSS • how to use software or table B of random digits to select a stratified random sample from the population when the strata are identified

A

SPSS

  1. assign a random number to each subject
  2. Transform –> compute variable
  3. Function Group “Random Numbers”
  4. Functions box: Rv.Uniform (creates (?,?) (create random numbers that fall between these two numbers (0,1)
  5. Target variable: “random”
  6. Dataset now has new variable, now sort
  7. Data –> sost cases –> move radnom to sort by
  8. make new variable “treatment group” put a 1, 2, 3 next to equal amounts of subject (i.e. first ten second ten third ten)
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46
Q

9 how to recognize whether a study is observational or an experiment

A

if the subjects are assigned to random groups, it’s an experiment

47
Q

9 how to identify the factors (aka explanatory variables), treatments, response variables, and individuals or subjects in an experiment

A

An explanatory variable is one that explains changes in that variable

48
Q

9 how to recognize bias due to confounding of explanatory variables with lurking variables in either an obervational study or an experiment

A

make sure that only the treatment varies across all groups

49
Q

9 how to outline the design of a completely randomized experiment

A

it should include size of groups, specific treatments and the response variable and be expressed as a flow diagram with arrows

50
Q

9 • SPSS • how to use software or table B to carry out the random assignment of subjects to groups in a completely randomized experiment

A

SPSS

  1. assign a random number to each subject
  2. Transform –> compute variable
  3. Function Group “Random Numbers”
  4. Functions box: Rv.Uniform (creates (?,?) (create random numbers that fall between these two numbers (0,1)
  5. Target variable: “random”
  6. Dataset now has new variable, now sort
  7. Data –> sost cases –> move radnom to sort by
  8. make new variable “treatment group” put a 1, 2, 3 next to equal amounts of subject (i.e. first ten second ten third ten)
51
Q

12 how to figure out the number of unique ways to choose r things out of n total things

A
52
Q

12 how to find the area of a triangle

A

(width x height)/2

53
Q

12 how to use probability rules

A
  1. Rule 1. The probability P(A) of any event A satisfies 0 ≤ P(A) ≤ 1.
  2. Rule 2. If S is the sample space in a probability model, then P(S) = 1.
  3. If A and B are disjoint, then P(A or B) = P(A) + P(B)
  4. If A and B are disjoint, then for any event A,
    * *P(A does not occur) = 1 − P(A)**
54
Q

13 deal with the probability question with phrase “at least”

A

then you do the multiplication of either the probability number if it’s of it happening or 1 - P if it’s of it NOT happening. (prob of no calls for flat in 4 calls = 1-(.28)(.28)(.28)(.28) or .994 (see prev card))

55
Q

13 How to determine the probability that both of two events A and B happen together

A

P(A and B) = P(A)P(B | A)

56
Q

13 how to find the probability that ALL of several events occur

A
57
Q

13 how to identify dependence vs independence

A

if you keep drawing from the same pool, thus changing the odds, that’s dependence. If P’s are independent, you can multiply them. (Probability that two calls for a flat tire (72% or .72 chance each) is .72 x .72)

58
Q

13 how to interpret the | symbol (the vertical bar) in a probability equation

A
  • think of it as “given the information that…” so
  • P (truck | imported)=0.546 would mean ““What proportion of imports are trucks?” whereas
  • P(imported | truck)=0.207 would mean “What proportion of trucks are imports?”
  • In other words, what proportion of the far one is the near one?
59
Q

13 how to use the multiplication rule for two random events

A

If A and B are independent, then P(A and B) = P(A)P(B)

60
Q

15 how to tell the difference between a parameter and a statistic

A

a parameter describes a whole population and is often unknowable, a statistic describes a sample

61
Q

15 how to sample distributions

A
  • Take a large number of samples of small size 10 from the population.
  • Calculate the sample mean x̄ for each sample.
  • Make a histogram of the values of x̄ .
  • Examine the shape, center, and variability of the distribution displayed in the histogram.
62
Q

15 how to draw a mean and standard deviation from a sample

A

the sampling distribution of x̄ has mean μ and σ/√n

63
Q

15.4 how to find the probability of getting a particular sample mean from a particular sample size

A

First compute the Z-score and look it up on the table, (remember to subtract from 1 for higher thans) and then use N(μ, σ/√n)

64
Q

16 • SPSS • how to use spss to calculate a confidence interval

A
  1. analyze > descriptive statistics > explore
  2. move continuous variable to dependent list
  3. click on statistics button to change 95% to 99% etc
  4. look at “Descriptives” output table
    5.
65
Q

16 how to determine the confidence interval of mean μ (under simple conditions)

A
66
Q

16 how to quickly find the number equivalents of z*

A
67
Q

17 how to define and distinguish z-test from p-value

A

The Z score is a test of statistical significance that helps you decide whether or not to reject the null hypothesis. The p-value is the probability that you have falsely rejected the null hypothesis. Z scores are measures of standard deviation. … Both statistics are associated with the standard normal distribution.

68
Q

17 how to identify WHEN to use a one sample z test

A
69
Q

17 how to perform a one sample z test

A
70
Q

17 z-procedures: to test H0: μ = μ0, we use the one-sample z statistic:

A
71
Q

17 how to calculate the z test statistic

A
72
Q

17 how to caluclate the P-value

A
73
Q

17 how to define significance tests

A
74
Q

17 how to evaluate whether evidence is sufficient to support or reject the null hypothesis

A
75
Q

17 how to plan null hypotheses versus alternate

A
76
Q

17 • SPSS • how to use SPSS for one sample z procedures

A
77
Q

17 how to use table A to find the P-value

A
78
Q

17 how to estimate a population parameter

A

Use a confidence interval

79
Q

17 how to evaluate p-value

A

Small P-values are evidence against H0 because they say that the observed result would be unlikely to occur if H0 were true. Large P-values fail to give evidence against H0. You might say, “an outcome that would occur so often when H0 is true is not good evidence against H0. The study looked for evidence against H0: μ = 0 and failed to find strong evidence. That is all we can say.”

80
Q

18 how to calculate the margin of error

A

m=z•sigma over square root of n

81
Q

18 how to calculate the right sample size

A

n=(z•sigma/m)2

82
Q

18 how to use a t table and why

A
83
Q

18.4 To obtain a desired margin of error m…

A

put in the value of z* for your desired confidence level, and solve for the sample size n

84
Q

20 how to find a one sample t confidence interval

A

To analyze samples from Normal populations with unknown σ, just replace the standard deviation σ/√n of x-bar by its standard error s/√n in the z procedures, then a level C confidence interval is this formula…

85
Q

20 how to find the standard error (the standard deviation when you only have a sample)

A
86
Q

20 how to find the one sample t-statistic (when you are using the error statistic to find the standard deviation)

A
87
Q

20.1 how to find the standard error and what it is

A

when you have to estimate the standard deviation from data, it’s called the standard error. you find the standard error of a sample mean like this:

s / √n

88
Q

21 how to define a t statistic

A

When you perform a t-test, you’re usually trying to find evidence of a significant difference between population means (2-sample t) or between the population mean and a hypothesized value (1-sample t). The t-value measures the size of the difference relative to the variation in your sample data. Put another way, T is simply the calculated difference represented in units of standard error. The greater the magnitude of T (it can be either positive or negative), the greater the evidence against the null hypothesis that there is no significant difference. The closer T is to 0, the more likely there isn’t a significant difference.

89
Q

21 How to determine a A level C confidence interval for

(unknown) μ1 − (unknown) μ2

A

`

90
Q

21 how to know when to use the hypothesis of no difference?

A

The hypothesis of no difference is used when investigating whether a treatment has an effect.

91
Q

21 • SPSS • how to perform paired T procedures for learning about a population mean

A
  • analyze > compare means > one sample t test
  • move response variable over to the “test variable window”
  • enter the “test value” (or null value)
  • hit okay
  • first box is sample data
  • second is one sample test incl t, df, and 2 sided P value (“Sig. 2-tailed)
  • BEWARE the confidence interval you see is not for the mean, if you wan that, go to analyze desc stat explore
92
Q

21 • SPSS • two independent sample mean t procedures

A
  • analyze > compare means > independent sample t test
  • put quantitative response into “test variable”
  • put two, labeled data sets in grouping variable
  • define groups
  • set confidence level under options
    *
93
Q

21 how to find the standard error, or estimated standard deviation, when we don’t know the poputlation standard deviations

A

Because we don’t know the population standard deviations, we estimate them by the sample standard deviations from our two samples. The result is the standard error, or estimated standard deviation, of the difference in sample means

94
Q

21 how to find the two-sample t-statistic

A

standardize the estimate by dividing it by its standard error

95
Q

22 how to define what p̂ measures

A

tests and confidence intervals for a population proportion p when the data are an SRS of size n.

96
Q

22 how to determine the approximate distribution for p̂ when there’s a large n

A
97
Q

22 how to find the margin of error in the large-sample confidence interval for p̂

A
98
Q

22 how to find the mean and standard deviation of the sample when finding p, a population proportion

A

the mean is p

the standard deviation is found with this formula

99
Q

22 how to find the the confidence interval for p̂

A
100
Q

22 how to know when to use p*

A

we use this when we have to guess at a proportion, so that we can determine the sample size. .05 yields the largest sample size, we use this when trying to get the desired margin of error

101
Q

22 how to perform a significance test for a proportion

A

to test the null hypothesis H0: p = p0…

102
Q

22 how to find the sample size for a desired margin of error

A

where p* is a guessed value for the sample proportion. The margin of error will always be less than or equal to m if you take the guess p* to be 0.5.

103
Q

25 how to calculate expected counts

A

To test H0, we compare the observed counts in the table with the expected counts, the counts we would expect—except for random variation—if H0 were true.

104
Q

25 how to determine the mean of any Chi-square distribution

A

it’s equal to its degrees of freedom

105
Q

25 how to explain the the chi-square statistic

A

To test whether the observed differences among the four distributions of living arrangements given age are statistically significant, we compare the observed and expected counts. The chi-square statistic is a measure of how far the observed counts in a two-way table are from the expected counts if H0 were true. The Chi-square statistic is a sum of terms, one for each cell in the table. Think of χ2 as a measure of the distance of the observed counts from the expected counts if H0 were true. Large values of χ2 are evidence against H0 because they say that the observed counts are far from what we would expect if H0 were true.

106
Q

25 how to find the degrees of freedom in a chi-squares distribution

A

The Chi-square distributions are a family of distributions that take only positive values and are skewed to the right. A specific Chi-square distribution is specified by giving its degrees of freedom.

You find the degrees of freedom by:

(# of rows-1)(# of columns)

107
Q

25 how to require minimumcell counts or the Chi-Square Test

A

You can safely use the Chi-square test with critical values from the chi-square distribution when no more than 20% of the expected counts are less than 5, and all individual expected counts are 1 or greater. In particular, all four expected counts in a 2 × 2 table should be 5 or greater. Note that these guidelines use EXPECTED counts.

108
Q

25 how to perform a chi-squares test for independence in SPSS

A
  • (if summarized as counts) data > weight cases
  • (if summarized as counts) move variable to “weight cases by” window, click OK
  • analyze > descriptive stats > cross tabs
  • determine row and column, click “statistics”
  • check chi-square > continue
  • click “cells”
  • check “expected” > continue
  • also check “clustered bar charts” at the bottom
  • click OK
  • middle chart is table
  • bottom right “asymptotic” is P-value
109
Q

27 how to determine the degrees of freedom for an ANOVA test

A

I = number of populations/means

N = number of total observations

so I-1/N-I

110
Q

27 how to find the ANOVA F statistic

A
111
Q

27 how to interpret the results of an ANOVA test

A

The results of the ANOVA F test are approximately correct when the largest sample standard deviation is no more than twice as large as the smallest sample standard deviation.

112
Q

27 • SPSS • how to perform a one-way ANOVA

A
  1. Analyze > Compare Means > one-way ANOVA
  2. plug in response/dependent and factor/explanatory
  3. click options
  4. check “descriptive” and “means plot”
  5. click continue and ok
  6. “Sig.” is P-value

Tukey:

  1. click Post-Hoc and Tukey
113
Q

15 • SPSS • one sample test and confidence interval

A
  • analyze > compare means > one sample t test
  • assign test variable
  • put null hypothesis into test value
  • options > pick confidence interval
  • continue > OK
  • to get one tailed value, divide sig. two tailed by 2

Intro Stats at UMass Lowell (20 decks)

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