Stats Final Exam Dr. Smith Cedarville

Parametric Test

A test that assumes a specific distribution of the populations involved.

Nonparametric Test

A test that is distribution free and does not require that samples come from populations with normal distribution or any other particular distribution.

Advantages of Nonparametric Test

1. Less rigid requirements applied to a variety of solutions. 2. Can be applied to more data types.

Disadvantages of Nonparametric Test

1. Wastes information; numerical data reduced to qualitative form. 2. Not as efficient (need stronger evidence).

Efficiency

Quality of solving the largest amount of work while using as little energy as possible.

Rank

Rank number assignment to an individual sample item according to its order in the sorted list.

Tie in Ranks

In the event of a tie, find the mean of ranks involved in the tie and assign the mean rank to each of the tied items.

Sign Test

A nonparametric test that can test claims about the median of a distribution.

Wilcoxon Signed-Ranks Test

A nonparametric test that can test claims about the differences between paired observations.

Wilcoxon Rank-Sum Test

A nonparametric test that can test claims about the differences between two independent groups.

Kruskal-Wallis Test

A nonparametric test that can test claims about the differences among three or more independent groups.

Rank Correlation Test

A test that assesses the strength and direction of the relationship between two ranked variables.

Random Variable

A variable (normally denoted as x) that has a single numerical value determined by chance for the outcome of a procedure.

Probability Distribution

A description that gives the probability for each value of a random variable.

Example of Ranks with Ties

In the sorted list 4,5,5,5,10,11,12,12, the ranks are assigned as follows: 4=1, 5=2,3,3,4, 10=5, 11=6, 12=7,7.5, 12=8,7.5.

Excel Sign Test

Instructions to conduct a Sign Test in Excel.

SPSS Sign Test

Instructions to conduct a Sign Test in SPSS.

SPSS Wilcoxon Signed-Ranks Test

Instructions to conduct a Wilcoxon Signed-Ranks Test in SPSS.

SPSS Wilcoxon Rank-Sum Test

Instructions to conduct a Wilcoxon Rank-Sum Test in SPSS.

SPSS Kruskal-Wallis Test

Instructions to conduct a Kruskal-Wallis Test in SPSS.

Excel Rank Correlation Test

Instructions to conduct a Rank Correlation Test in Excel.

SPSS Rank Correlation Test

Instructions to conduct a Rank Correlation Test in SPSS.

Significant high number of success

More than .05

Significant low

Fewer than .05

Rare Event Rule

The probability of a particular observed event is extremely small, we conclude that the assumption is probably not correct.

Binomial probability distribution outcomes

The number of possible outcomes is determined by the number of trials, (n). Specifically, there are (n + 1) possible outcomes, ranging from 0 successes to (n) successes.

Example of binomial outcomes

If you have 5 trials, the possible outcomes are 0, 1, 2, 3, 4, and 5 successes, making a total of 6 possible outcomes.

Range rule of thumb

s~R/4 helpful in understanding meaning of mean and standard deviation.

Continuous probability distribution

The area under the curve equals 1, therefore there is a correspondence between area and probability.

Z score

A z-score represents how many standard deviations a raw score is above or below the mean.

Area in standard normal distribution

Area represents the probability under the curve, essentially equal to the probability associated with that range of values.

At most

The maximum possible value that a variable can take.

No more than

Means that a value is less than or equal to a specific limit.

At least

Means the minimum possible value or count of a certain event that can occur.

Z score interpretation

How many standard deviations are away from the mean.

Z score critical values

A specific point on the standard normal distribution that marks the boundary between the region where a test statistic is considered statistically significant and where it is not, based on a chosen significance level (alpha).

Formula 6-2

Used to convert values to Z scores in order to find probabilities.

Significantly high or low values

Determined by comparing the calculated Z score to critical values.

Miu

Represents the mean in probability calculations.

Standard deviation symbol

The symbol at the bottom of the formula represents standard deviation.

Figures 6-16 and 6-17

Refer to specific illustrations on p 277, disregarding the Variances portion.

Central Limit Theorem

A statistical theory that states that the distribution of sample means will be approximately normal if the sample size is large enough.

Z score

A statistical measurement that describes a value's relation to the mean of a group of values, calculated by subtracting the mean and dividing by the standard deviation.

Rare Event Rule for Inferential Statistics

A principle stating that if an event is rare, it is unlikely to occur by random chance alone.

Point Estimate

A single value used to estimate a population parameter, such as the best point estimate of population proportion p.

Confidence Interval

A range of values used to estimate the true value of a population parameter.

Confidence Level

The probability that the confidence interval actually contains the population parameter, assuming the estimation process is repeated a large number of times.

Critical Value

A number on the borderline separating sample statistics that are significantly high or low from those that are not significant.

Margin of Error

The maximum likely amount of error when estimating a population proportion, denoted by E.

Sample Size Requirement

According to the Central Limit Theorem, if the sample size is large enough (typically n > 30), the distribution of the sample mean will be approximately normal.

Student t Distribution

A type of probability distribution that is symmetric and bell-shaped, similar to the normal distribution but with heavier tails.

Degrees of Freedom (df)

Typically the sample size minus one (n - 1), used in statistical calculations.

Confidence Interval Formula

Confidence Interval = x̄ ± t*(s/n^1/2)

Confidence Interval for a Proportion

A method to construct a confidence interval for a proportion using specific statistical formulas.

Normal Quantile Plot

A graphical tool used to evaluate the normality of a dataset.

Sample Mean

The best estimate of the population mean, calculated as the average of sample data.

t-Distribution Table

A table used to find critical values for the t-distribution based on degrees of freedom and confidence level.

Sampling Method

The technique used to select a sample from a population, which affects the quality of poll results.

Simple Random Sample

A sample that is chosen randomly from a population, ensuring that every individual has an equal chance of being selected.

Confidence Level Examples

Common confidence levels are 90%, 95%, and 99%, determining the area in the tails of the distribution.

Four Points in Analyzing Polls

1. Sample should be a simple random sample, not an inappropriate sample. 2. Confidence level should be provided. 3. Sample size should be provided. 4. Quality of the poll results depends on sampling method.

Confidence Interval

Use sample data to construct and interpret a confidence interval estimate of the true value of a population mean µ.

Sample Size

Find the sample size necessary to estimate a population mean.

µ

Population mean.

n

Number of sample values.

Data

Collections of observations, such as measurements, genders, or survey responses.

Statistics

Science of planning studies and experiments; obtaining data; and organizing, summarizing, presenting, analyzing, and interpreting those data and then drawing conclusions based on them.

Population

Complete collection of all measurements or data that are being considered.

Census

Collection of data from every member of the population.

Sample

Subcollection of members selected from a population.

Statistical Significance

Achieved in a study when we get a result that is very unlikely to occur by chance.

Practical Significance

It is possible that some treatment or finding is effective, but common sense might suggest that the treatment or finding does not make enough of a difference to justify its use or to be practical.

Parameter

Numerical measurement describing some characteristic of a population.

Statistic

Numerical measurement describing some characteristic of a sample.

Qualitative (Categorical)

Consists of names or labels.

Quantitative

Consists of numbers representing counts or measurements.

Discrete Data

Results when the data values are quantitative and the number of values is finite, or 'countable.'

Continuous Data

Results from infinitely many possible quantitative values, where the collection of values is not countable.

Nominal Data

Categories only; data cannot be arranged in order.

Ordinal Data

Data can be arranged in order, but differences either can't be found or are meaningless.

Interval Data

Differences are meaningful, but there is no natural zero starting point and ratios are meaningless.

Ratio Data

There is a natural zero starting point and ratios make sense.

Skewed to the Right

Have a longer right tail.

Skewed to the Left

Have a longer left tail.

Mean

One of the three measures of center.

Median

One of the three measures of center.

Mode

One of the three measures of center.

Resistant

Refers to a measure that is not affected by extreme values.

Resistant

The presence of extreme values (outliers) does not cause it to change very much.

Range

Range = (MAXIMUM DATA VALUE) - (MINIMUM DATA VALUE)

Standard Deviation

Set of sample values, denoted by s, is a measure of how much data values deviate away from the mean.

Population Standard Deviation

Denoted by σ.

Sample Standard Deviation

Denoted by s.

Population Mean

Notation for population mean: μ.

Sample Mean

Notation for sample mean: x̄.

Z Score

A z score allows you to compare a data value to the mean of a data set.

Significantly Low Z Score

A data value is significantly low if its z score is less than or equal to -2.

Significantly High Z Score

A data value is significantly high if its z score is greater than or equal to +2.

Percentiles

Percentiles are measures of location that divide a data set into 100 equal parts, with each part representing approximately 1% of the data values.

Quartile

Measures of location which divide a set of data into four groups with about 25% of the values in each group.