Descriptive Stats & Statistical Inference

What are categorical/qualitative variables?

Any assigned numerals the represent categories (ranked or unranked)

What kind of variables are limited statistically?

Categorical/qualitative variables

What are the different types of categorical/qualitative variables?

• Nominal

• Ordinal

What are nominal variables?

• A type of categorical/qualitative variable

• Entities divided into 2+ distincted UNRANKED categories

The following is an example of what kind of variable?

Type of hip replacement surgery (0 = anterior, 1 = posterior)

Nominal

What is an ordinal variable?

• A type of categorical/qualitative variable

• 2+ ORDERED/RANKED categories

The following is an example of what kind of variable?

Self rated health (1 = poor, 2 = fair, 3 = good, 4 = very good)

-Ordinal

What is an important thing to do when working with categorical/qualitative variables?

Distinguish actual variable from levels of the variable

What are numeric quantitative variables?

Numbers that represent an amount/quantity of an entity and not a category or ranking

What are the different types of numerica/quantitative variables?

• Discrete

• Continuous

What is a discrete variable?

• A type of numerica/quantitative variable

• Variables that can only take on specific values within a give range (whole interger units)

The following is an example of what variable?

Number of tibial fractures

Discrete variable

What is a continuous variable?

• A type of numeric quantitative variable

• Variable where scores occur along a continuum in theory but is constrained by precision of measuring intstrument

The following is an example of what variable?

Distance walked (in meters) during a 6MWT

Continuous variable

Define parametric testing

Testing that assumes data is normally distributed in a bell shape pattern

Which type of testing is more powerful, parametric or nonparametric testing?

Parametric testing

Parametric testing is used with what kind of data with what kind of distribution?

Quantitative data w/ a normal distribution

What kind of testing can you assume normality?

Parametric testing

What kind of testing can you not assume normality?

Nonparametric testing

What kind of data is used in nonpararmetric testing?

• Categorical data

• Quantitative data that don’t go a normal distribution

What kind of graphs could you use when you have continuous/quantitative data?

• Boxplot

• Error bar chart

• Histogram

• Q-Q/P-P plot

• Stem-and-leaf plot

What kind of stat procedure can you use for either continuous/quantitative or categorical variables?

Frequency table

What kind of stat procedures can you use for continuous/quantitative variables?

• Descriptive stats

  • N

  • Mean

  • SD

  • 5 numbers ummary

    • Min

    • 1st quartile

    • Median

    • Max

• 1 Sample t-test

• Freq table

What kind of graphs can you use when you have categorical variables?

• Bar chart

• Pie chart

What kind of stat procedures can you use if you have categorical variables?

• Freq table

• Binomial test

• Chi-sq goodness of fit

What do descriptive stats characterize?

• Shape/distribution within a set of data

• Central tendency within a set of data

• Dispersion/variability within a set of data

What is the first step in the data analysis process?

Checking shape/distribution of data

Why do you need to do data anlysis process?

• Gives us a sense of the data

• Informs decisions about normality and parametric v non parametric testing

What are some visual checks you can do to examin distribution and evaluate normality?

• Histograms

• Stem-and-leaf plots

• P-P plots

• Q-Q plots

What needs to be done prior to any further statistical analysis with quantitative variables?

Checking for normality

What are some numeric checks for examine distribution and evaluating normality?

• Frequency tables

• Values for skweness and kurtosis

• Statistical tests for normality

  • K-S test

  • S-W test

What is a histogram?

A graph plotting values of observations on the horizontal axis with a bar showing how many times each value occured in the data set

What is on the x axis of a histogram?

Values of observations

What is on the y-axis of a histogram?

Frequency

What does a scew mean?

A distripution is asymmetrical and normality assumption cannot be met

What is a positive skew?

When scores are bunched at low values w/ the tail pointing to high values

What is a negative skew?

When scores are bunched at high values with the tail pointing to low values

What is kurtosis?

The “peakedness” and degree to which scores cluster at tails

What is positive kurtosis/leptokurtic?

When a histogram is too peaked and has real long tails

What is negative kurtosis/platykurtic?

When a histogram is too flat and has short tails

What is a Q-Q plot?

A quantile-quantile plot. Plot of quantiles of variable v quantiles of a theoretical distribution

What is on the y-axis of a Q-Q plot?

The expected data in SPSS

What is on the x-axis on a Q-Q plot?

The observed data in SPSS

What would indicate data normality on a Q-Q plot?

The data falls along a straight line on a plot

What does kurtosis look like on a Q-Q plot?

The data is consistently sagging above or below the line

What does skewness look like on a Q-Q plot?

Data is s-shaped around the line

Positive values on a Q-Q plot indicate…

Positive skew/kurtosis

Negative values on a Q-Q plot indicate…

Negative skew/kurtosis

The further values are from 0 on a Q-Q plot, the more…

Skew/kurtosis there is

How do you convert a skewness/kurtosis value to a z-score?

Divide the skewness/kurtosis value by its standard error

If the absolute value of a z-score is greater than _____, then it is sigificantly different from 0 and is NOT dormally distributed

1.96

A z-score has to be under what number to be considered normally distributed?

Under 1.96

What is the most common way to check for normality?

• Kolomogrov-Smirnov (K-S) test

and

• Shapiro-Wilk (S-W) test

When running a K-S or S-W test, what does p need to be less than to be considered significantly different from a normal distribution?

Less than .05

When running a K-S or S-W test, what does p need to be greater than to indicate that the data is normally distributed?

Greater than .05

The S-W test is better for studies with how many samples?

Less than 50

What are 3 common measures to calculate where the center of a distribution lie?

• Mode

• Median

• Mean

What is the mode?

The most frequent score

What is the mode useful for?

Summarizing categorical data

What is a downside of the mode?

It can take on several values

What is the median?

THe middle score when you order the data

What is the median useful for?

• Ordinal data

• Quantitative data

The median is preferred over what other method of central tendency when working with skewed distributions or data with outliers?

Mean

What is the mean?

The average score

What is a downside of using the mean?

Not useful for categorical data or for quantitative data that is skewed or has outliers

List the measures of dispersion/variability in a distribution

• Range

• Quantiles

• Variance

• Standard deviation

• Coefficient of variation

What is the range?

The largest score minus the smallest score

What are quantiles

Equal data splits

What is the interquartile range?

Upper (3rd) quartile minus lower (1st) quartile

What are all the parts of a 5-point/number summary?

• Minimum

• 25th percentile (lower quartile)

• 50th percentile (median)

• 75th percentile (upper quartile)

• Max

Define deviance

How different a score is from the center of a distribution

What does the sum of squares (SS) or mean squared error represent?

The total dispersion or total deviance of scores from the mean

What is the sum of squares (SS) or mean squared error dependent on?

The number of scores in the data

What is the term for the average dispersion?

Variance

Variance gives us a value in units ____

Squared

If you have variance, how can you get to SD?

By square rooting the variance

If you have SD, how can you get to variance?

Squaring SD

What is the coefficient of variation (CV)?

The ratio of standard deviation to mean expressed as a percentage

The coefficient of variation (CV) has no units. True or false?

True

Why is it helpful that the coefficient of variation (CV) does not have any units?

It allows us to compare distributions from different saples that may have different means or units

In a boxplot, any points outside of ____ are considered outliers

Whiskers

Statistical inference is based on what assumption?

That sample data represents population characteristics

The assumption for statistical inference is based on what concepts?

• Probability (the likelihood that an event will occur given all the possible outcomes)

• Sampling error (extent to which a statistic varies in samples taken from the same population

What percentage of the population is within 1 SD of the mean?

68.26%

What percentage of the population is within 2 SD?

• 95.44%

  • 95% within 1.96 SD

What percentage of a population is within 3 SD?

99.74%

What does a z-score represent?

How many SDs a score is away from the mean

What is a sampling error?

The difference/deviance between each sample mean and ppulation mean

Do you want a big sampling or small sampling error?

Small

What is a standard error of mean (SEM)?

The SD of a distribution of sampling distribution

What does a standard error of mean (SEM) indicate?

How close a sample mean is to the true population mean

What is a confidence interval?

The range within we believe the true population paramter lies

What is the z-score for a 95% CI?

1.96

Statistical tests are based on _____ hypothesis

Null

If p is less than or equal to 0.05, do you reject the null and accept the alternative or accept the null and reject the alternative?

• Reject null

• Accept alternative

If p is greater than 0.05, do we fail to reject the null or alternative?

Fail to reject the null

What is a type 1 error?

When you reject the null but it’s actually true

Is alpha or beta the probability of making a type 1 error?

Alpha

What is a type II error?

Wen you fail to reject the null when the null is actually false

Is alpha or beta the probability of making a type II error?

Beta