Example 1

Students in an introductory statistical class participated in an experiment

simple. Each student recorded their pulse in the resting position. Then everyone

Coin and those who got face ran on the site for a minute. TO

Then the whole class recorded its pulses. You want to examine the frequencies of

Pulse at rest of the students.

1 Open the PULSE.MTW worksheet.

2 Choose Statistics> Basic Statistics> Graph Summary.

3 Under Variables, enter Pulse1. Click OK.

Output of the Graph window

Interpretation of results:

The mean resting pulse of the students is 72,870 (95% confidence intervals

70,590 and 75,149). The standard deviation is 11,009 (95% confidence intervals of 9,615

And 12,878).

When a significance level of 0.05 is used, AndersonDarling's normality test

(A-square = 0.98, p-value = 0.013) indicates that the rest pulse data does not

Follow a normal distribution.

Normal Test.

Generates a normal probability graph and performs a hypothesis test to examine

Whether or not observations follow a normal distribution. For the normality test, the

Hypotheses are,

H0: the data follow a normal distribution vs. H1: data does not follow a distribution

Normal

The vertical scale of the graph resembles the vertical scale of the probability paper

normal. The horizontal axis is a linear scale. The line forms an estimate of the

Cumulative distribution for the population from which the data were extracted. With the graph

Numerical estimates of the population parameters, m and s, the value of

The normality test and the associated p-value.

Dialog Box Items:

• Variable: Enter the column to be used for the x-axis. Minitab calculates the

Probability of occurrence of each observation in the column (assuming one,

Normal distribution) and uses the logarithm of the probabilities calculated as

Values ​​and.

• Percentile lines: Minitab marks each of the percentages in the column with

A horizontal reference line on the graph and mark each line with the value

percentage. Minitab draws a vertical reference line, in which the line of

Horizontal reference intersects the fit of the line to the data, and marks this line

With the estimated data value.

• None: Choose this option to display no percentile line.

• In Y values: Choose this option to enter Y values ​​to place values

The percentile lines. Enter values ​​between 0 and 100 when percentages are

Use as the scale type Y, or 0 to 1 when the probability is the scale type

Y.

In data values: Choose this option to enter data values ​​to place

Percentile lines.

• Anderson-Darling: Choose this option to perform an Anderson-Darling test of

Normality, which is a test based on ECDF (distribution function

Accumulated empirical).

• Ryan-Joiner: Choose this option to perform a Ryan-Joiner test, which is similar

To the Shapiro-Wilk test. The Ryan-Joiner test is a test based on

Correlations.

• Kolmogorov-Smirnov: Choose this option to test Kolmogorov-Smirnov

Of normality, which is a test based on ECDF.

• Title: To replace the default title with its own custom title,

Type the text you want in this box.

Example 2:

On a running engine, the camshaft parts rise and fall. DistAaB is the

Distance (in mm) from the actual position (A) of a point on the camshaft to a

Baseline position (B). To ensure the quality of production, a manager took five

Measurements every day of work in a plant assembling of vehicles, from the 28 of

September until October 15, and then ten measurements a day from the 18th to the 25th of

September.

You want to determine if these data follow a normal distribution, so you use

A test of normality.

1 Open the ARBOLLEV.MTW worksheet

"You must do the steps so that you can see the graph and interpret the following"

Interpretation of results

The graphical output is a graph of normal probabilities versus data. The data are

Away from the adjusted line more clearly at the ends, or tails of the

distribution. The p-value of the Anderson-Darling test indicates that, at higher levels

Than 0.022, there is evidence that the data do not follow a normal distribution. There is a

There is a slight tendency for the data to be lighter in the queues than the normal distribution

Because the smaller points are below the line and the longest point

Large is above the line. A distribution with heavy tails would show

An opposite pattern at the ends.

Show Descriptive Statistics

Produces descriptive statistics for each column, or for each level of a per variable.

To calculate descriptive statistics individually and store them as constants,

See Column Statistics. To store a wide variety of statistics, use

Store descriptive statistics.

Use Show Descriptive Statistics to produce statistics for each column or

For subsets within a column. You can display these statistics in the

Window and optionally on a graph (see Descriptive Statistics

Available for display or storage).

Dialog Box Items

Variables: Choose the columns you want to describe.

By variables (optional): Enter the column containing the variables for display

Descriptive statistics separately for each value of the specified variable. The

Columns must have the same length. For the limitations associated with the use of a

Variable, see Graph Limits.

Choose the statistics you want to display.

Dialog Box Items

• Median: Choose this option to display the arithmetic mean.

• Median EE: Choose this option to display the standard media error.

• Standard deviation: Select this option to display the standard deviation of the

data.

• Variance: Choose this option to display the variance of the data.

• Coefficient of variation: Choose this option to display the coefficient of variation.

• First Quartile: Choose this option to display the first quartile.

• Median: Choose this option to display the median.

• Third Quartile: Choose this option to display the third quartile.

• Interquartile Range: Choose this option to show the difference between the first and

Third quartile.

• Fashion: Choose this option to show the fashion and the number of times it occurs. Yes

There are multiple fashions, Minitab shows the smallest fashions, up to a total

Of four, along with their frequencies.

• Cropped Media: Choose this option to display the cropped media.

• Sum: Select this option to display the sum of the data.

• Minimum: Choose this option to display the minimum of the data.

• Maximum: Choose this option to display the maximum of the data.

• Range: Choose this option to display the range of the data.

• Number of values ​​present: Select this option to display the number of values

Present column entries.

• Number of missing values: Select this option to display the number of values

Missing column entries.

• Number of total observations: Choose this option to display the total number of

Values ​​(present and missing) of column entries.

• Cumulative Number: Choose this option to display the accumulated number of

tickets.

Percentage: Choose this option to show the percentage of observations that

It is a group The percentage will be 100 unless you use one per

variable.

• Cumulative Percentage: Choose this option to display the cumulative percentage.

• Sum of squares: Choose this option to display the sum of the values ​​of the data

Elevated to the square. This is the sum of uncorrected squares, without first subtracting

Average

• Asymmetry: Choose this option to display the asymmetry value.

• Curtosis: Choose this option to store the kurtosis value

• MSSD: Choose this option to store half of the mean of the differences

Successive squares.

Mark Statistics

O Default: Choose this option to mark the statistics set

Default as specified in Tools> Options>

Individual commands> Show descriptive statistics. You can

Check the uncheck the statistics as needed.

O None: Select this option to uncheck all check boxes and

So you can individually mark the statistics you want to display.

Or All: Choose this option to check all the check boxes. You

You can deselect statistics as needed.

show a histogram, a histogram with a normal curve, a graph of values

And a cash chart.

Dialog Box Items

• Data Histogram: Choose this option to display a histogram for each

variable.

• Data histogram, with normal curve: Choose this option to display a

Histogram with a normal curve for each variable.

• Graph of individual values: Choose this option to display a graph of values

For each variable.

• Data Box Graph: Choose this option to display a box chart for each

variable

Example 3:

You want to compare the height (in inches) of male students (Sex = 1) and females

(Sex = 2) who participate in a pulse study. You choose to display a box chart

Of the data.

1 Open the PULSO.MTW worksheet

Show Descriptive Statistics

Interpretation of results

The averages shown in the Session window and the box charts indicate that the

Males are about 5.3 inches taller than females, and that the dispersion

Of the data is approximately the same.

Histogram

Use this option to display multiple histograms or multiple adjusted curves

(Probability density functions, pdfs) on the same graph.

Dialog Box Items

• Graph Variables: Enter one or more columns of data to graph. By choice

Minitab draws each column on the same graph.

• Categorical variables for grouping (0 to 3): If the columns of the variables of

Graphs contain multiple groups, enter up to three columns of variables

Categorical for grouping. (To display in panels of one or more variables,

Use By Variables.

• Graph variables form groups: Check this option to show

Histograms of all graph variables on the same graph. (To show

All graphs on the same page, use Multiple Variables).

<Scale>

Axes and brands

Scale Type Y

Grid lines

Reference lines

<Tags>

Title / footnotes

Data Labels

<Show data>

Data presentation

Lowess

Distribution

<Multiple Graphics>

Multiple variables

By variables

By variables (area graphs, time series graphs)

<Data Options>

Subset

Group Options

Frequency

Example 4:

Simple Histogram

You work for a shampoo factory and you need to make sure that the

Bottles are set correctly. If they are not tight, they may fall

During shipment. If they are too tight, your customers are likely to have

Difficulty opening them (especially in the shower).

You collect a random sample of bottles and test the amount of torque required

To remove the lids. Create a histogram to evaluate the data and determine how close

Are the target value samples of 18.

1 Open the TAPA.MTW worksheet

Choose Histogram Graph

Interpretation of results

Most of the lids were adjusted with a twist of 13 to 25. Only one of the lids

Was very loose, with a torque less than 11. However, the distribution is

Positively asymmetric; Several caps were much tighter than they should have been. For

Remove many of the caps, required a twist greater than 24 and five caps required

A torsion greater than 33, almost twice the target value

Example 5:

Histogram with adjustment:

You work for a shampoo factory and you need to make sure that the

Bottles are set correctly. If they are not tight, they may fall

During shipment. If they are too tight, your customers are likely to have

Difficulty opening them (especially in the shower).

You collect a random sample of bottles and test the amount of torque required

To remove the lids. Create a histogram with an adjusted normal distribution to evaluate

How accurately their samples reached the target value of 18 and if the data are

Normally distributed.

1 Open the TAPA.MTW worksheet

Interpretation of results:

The mean torsion for the sample was 21.26, slightly higher than the target value of

18. Only one cover was very loose, requiring a torque of less than 11. However, the

Distribution is positively asymmetrical, and several caps were much

due. To remove many of the lids, a twist greater than 24 and five lids were required

Required a torque greater than 33, almost twice the target value.

Because the sample data is so asymmetrical, the normal distribution does not adjust

adequately.

Example 6:

Histogram with outline and groups

You work in an automobile factory and you have problems with the

Variability in the length of the camshafts used. You want to determine if the

Camshafts supplied by its two suppliers are similar, so it measures

The length for a random sample of 100 camshafts of each. Create a

Histogram to compare the lengths of the camshafts of the two suppliers.

1 Open the worksheet ARROLLEVAS.MTW

Interpretation of results:

The average lengths of the camshafts of the two suppliers appear to be similar.

However, there is much more variability in the length of the trees supplied by the

Provider 2. It appears that Provider 2 is to blame for its problems of discrepancy in

The length of camshafts. When comparing distributions with histograms, it can be

Easier for you to split them into panels. See Bar Edit Examples.

EXAMPLE 7

Histogram with adjustment and groups.

You work in an automobile factory and you have problems with the

Variability in the length of the camshafts used. You want to determine if the

Camshafts supplied by its two suppliers are similar, so it measures

The length for a random sample of 100 camshafts of each. Create a chart

With overlapping adjusted normal distributions of the data to compare the

Samples from the two suppliers.

1 Open the worksheet ARROLLEVAS.MTW

Interpretation of results

The camshafts of Provider 1 are apparently shorter than those of Provider 2. This

Is indicated by the averages in the table (599.5 and 600.2, respectively), as well as the position

Relative of the peaks of the adjusted normal distributions.

The standard deviation of the Supplier 2 sample (1.874) is much higher than that of the

Provider 1 (0.6193). This translates into a shorter and broader adjusted distribution

For Supplier 2. The great variability of Supplier 2 products can be the

Main cause of their problems of discrepancy in the length of the camshafts.

Use the box charts (also called box charts and whiskers) to evaluate and

Compare the distributions of the sample.

Example 8 :

Simple cash chart

You want to examine the overall durability of your carpet products. The samples

Of carpet products are placed in four homes and you measure durability

After 60 days. Create a box chart to examine the distribution of

Durability ratings.

1 Open the ALFOMBRA.MTW.worksheet.

Interpretation of results

Suggestion. To obtain accurate information on Q1, median, Q3, interquartile range,

Mustaches and N, place the cursor over any part of the box graph.

The box graph shows:

· The median durability score is 12.95.

· The interquartile range is from 10.575 to 17.24.

· Atypical values ​​are not present.

· The range is from 7.03 to 22.5.

· The longest top mustache and large box area located above the median

Indicate that the data have a slightly positive asymmetry - the right tail of

The distribution is longer than the left tail

Example 9:

Cash chart with groups.

You want to evaluate the durability of four experimental carpet products. The

Samples of carpet products are placed in four homes and you

Durability after 60 days. Create a box graph with median labels and boxes Color coded to examine the durability distribution of each Carpet.

1 Open the ALFOMBRA.MTW.worksheet.

Interpretation of results

The median durability is highest for Carpet 4 (19.75). However, this product

Also shows the greatest variability, with an interquartile range of 9,855. Besides, the

Distribution has a negative asymmetry, with at least one durability measurement of

Approximately 10.

Carpets 1 and 3 have similar durability medians (13.52 and 12.895,

respectively). Carpet 3 also shows the lowest variability, with a range

Interquartile range of only 2.8925.

The median durability of Carpet 2 is only 8,625. This distribution and that of the

Carpet 1 have positive asymmetry, with interquartile ranges of approximately 5-6.

Suggestion. To obtain accurate information on Q1, median, Q3, interquartile range,

Mustaches and N, place the cursor over any part of the box graph.

Example 10:

Multi-Y Box Graph

Your company manufactures plastic tubes and you are interested in the uniformity of diameters.

You measure ten tubes a week for three weeks. Create a box chart for

Examine the distributions.

1 Open the  TUBERÍA.MTW worksheet.

Interpretation of results

Suggestion

To obtain accurate information on Q1, median, Q3, interquartile range, whiskers and N,

Place the cursor over any part of the box graph.

The box graph shows:

· The median for Week 1 is 4,985, and the interquartile range is 4.4525 to 5.5575.

· The median of Week 2 is 5,275, and the interquartile range is 5.08 to 5.6775.

An atypical value appears in 7.0.

· The median of Week 3 is 5.43, and the interquartile range is 4.99 to 6.975. The

Data are positively asymmetrical.

The medians of the three weeks are similar. However, during Week 2,

Manufactured an abnormally wide tube, and during Week 3, several tubes were made

Abnormally wide.

Example 11:

Box graph with multiple Y and groups.

Your company manufactures plastic tubes and you are interested in the uniformity of diameters.

You measure ten tubes of each machine per week for three weeks. Create a chart

To examine the distributions.

1 Open the  TUBERÍA.MTW worksheet.

Interpretation of results

The box graph shows:

· For machine 1, the median diameter and variability seems to increase each week.

· For machine 2, the median diameter and variability seems to be more stable between

the weeks.

Statistical analysis, such as balanced man-

To examine more closely the relationship between factors.

Suggestion. To obtain accurate information on Q1, median, Q3, interquartile range,

Mustaches and N, place the cursor over any part of the box graph. To see the value

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