Foundation of Statistics with Minitab

From the lecture:

"In this tutorial we will begin the process of analyzing data by learning how Minitab can be used to explore and summarize data for a single variable, numerically.

First, we deal with qualitative variables. In this demonstration we use the Infants worksheet where the data are part of a research where we have been conducting a study of the factors that appeared to be associated with a new mother's decision to breastfeed her infant or not. 68 low income pregnant women who attended a clinic affiliated with a group are the subjects.

Our task is to summarize the data collected on these women and their new born children. "

From the lecture:

"If we want to graphically represent the percentage associated with the category, we have two ways to do this: the bar chart and the pie chart. Now, let's begin with the bar chart. "

From the lecture:

"Now we will use Minitab to find numerical summaries for quantitative variables.

We are going to start by looking at descriptive statistics for the time the pregnant women spent with a nutritionist before their childbirth, before their delivery."

From the lecture:

"Minitab offers a number of graphs designed to display quantitative data.

In this section we will examine histograms."

From the lecture:

"Stem-and-Leaf Display of quantitative data enables us to see the actual data while retaining much of the same features of a histogram.

It is an example of a character graph. The numbers in the centre column represents the stems or left most digits of the data values. The column on the right contains the leaves because Minitab records a leaf unit of one. Each leaf represents the one's digit of a data value, and each stem represents the ten's digit of the data value. "

From the lecture:

"Now we will look at a dot plot and an individual value representation of data. "

" The scattering of the points allows for each point on the display to represent exact values. "

From the lecture:

"A boxplot provides us with rather skeletal view of our data set. "

"A boxplot uses five numbers to describe a set of data. The maximum value, the 3rd Quartile, the Median, the 1st Quartile and the minimum value. Collectively these five numbers are known of the 5-number summary of the data set.

Minitab constructs a rectangle, a box between the 1st and the 3rd Quartiles and displays a horizontal line at the location of the Median. This box encloses the middle half of the data. The Whiskers that extend either direction indicate the non-outlying data. If there no outlier values, the whiskers extend to the smallest and the largest values in the data set."

From the lecture:

"In this tutorial we will construct tables to compare groups based upon two qualitative variables.

We will examine the smoking status of 68 pregnant women who participated in a clinical study. Their data are recorded in the Infants data file. First, investigate the relationship between smoking status and ethnicity because both of these variables are qualitative. We explore the relationship between them by obtaining a two-way table of counts called a Contingency Table. Sometimes this table is called a Cross Tabulation Table. "

From the lecture:

"Here we will construct bar charts to represent relationship between two categorical variables. We will use one of the variables as a so-called cluster or grouping variable.

We will use the file Infants, and we will construct two bar charts between the variables Smoke and Ethnic, and we define Ethnic as a Cluster Variable."

From the lecture:

"Minitab allows us to compare subgroups of quantitative variables by showing different graphs separately for each subgroup.

As an illustration we will use the data in the BallPark data worksheet. Here, in this worksheet the data relate to the 30 Major League baseball teams."

From the lecture:

"We can get summary statistics for several quantitative variables simultaneously and in this way we can compare subgroups using numerical descriptive measures.

Now, we use the BallPark data again."

From the lecture:

"The Bar Chart command can be used to produce many kinds of displays of Summary Statistics.

To explore this capability, we use the BallPark data worksheet. Here, the data relate to the 30 Major League baseball teams."

From the lecture:

"Generally, the best way to begin an exploration of the relationship between the quantitative variables is to construct a co-called scatterplot. This is a two-dimensional graph in which each value is represented by a single dot."

From the lecture:

"A marginal plot combines the features of a scatterplot with some of the one variable graphs. It means that we can examine the relationship between two variables while also viewing the distribution of each variable, all on the same graph."

From the lecture:

"The covariance and the correlation coefficient are numerical measures of the strength of the linear relationship between two quantitative variables. "

"A positive covariance suggests that high values for one variable tend to be associated with high values for the other. However, because the value for the covariance depends on the units associated with the two variables, it is difficult to determine the exact strength of the relationship from this value.

Pearson's Correlation Coefficient or simply the Correlation Coefficient measures the strength of the linear relationship between two quantitative variables in a way that it does not depend on the units of the two variables. It is usually designated by small or lower case "r", and always lies between -1 and +1. In fact, "r" is the covariance divided the product of the standard deviations of the variables. "

From the lecture:

"While Correlation Coefficient measures the strength of the linear relationship between two quantitative variables, the Regression Line or Least-Squares Line summarizes the form of this relationship."

From trhe lecture:

"Binomial Distribution comes up when we repeat the so-called Trial more times in succession.

A Trial is the most basic type of a Random Experiment when the experiment has only two outcomes, usually called Success and Failure, and while repeating this trial more times, the probability of getting success or failure remains unchanged.

So, Binomial Distribution is specified by two parameters, "n", small "n", the number of trials and "p", small "p", the probability of success on each trial. The Number of Success can be 0, 1, 2, and so on, up to "n".

As an example, find out the probability of getting 3 successes when p is 1/6 and n is equal to 10. "

From the lecture:

"Poission Distribution arises when we count the number of Occurrences of an Event relatively infrequently. This distribution is completely specified by just one parameter by the Mean of the number of occurrences.

For example, if we know that in a city there are, on average, 6 accidents per weekend, then we can calculate the probability there will be, say, 5, 10 or 20 accidents next week, or no accidents at all. "

From the lecture:

"In this section we will use some of the Minitab's capabilities related to calculating and graphing, plotting probabilities of random events. let's assume, for example, that the heights of people in a group has normal distribution with mean µ is equal 170 centimeters, and with standard deviation σ is equal 10 centimeters.

Now, calculate probabilities of events related to the random experiment when we select 1 person randomly from this group. "

From the lecture:

"In inferential statistics we often need to determine certain values of a random variable called as critical values which refer to a predefined probability. The chance to get a larger or alternatively smaller value as an outcome of the experiment than the critical value is equal to this predefined probability.

Let's assume, for example, that the heights of people in a group is normally distributed with Mean 170 centimeters and with Standard Deviation, σ, is equal 10 centimeters. Now, let's determine that distinct value of heights called Right Tail Critical Value, for which it's true that the probability of randomly selecting one such person from this group, who is taller than this value, is equal, let's say, 10%. "

From the lecture:

"The family of normal distributions, sometimes we call them Bell-Shaped Curves, plays a central role in Statistics. In this section we will generate a sample from a Normal Distribution and check the Normality of this sample.

First, simulate the selection of a random sample of heights of people using the Mean Value, µ, which is equal to 170 centimeters, and Standard Deviation, σ, whics is equal to 10 centimeters."

From the lecture:

" In this tutorial we will simulate the process of sampling when we take more than one sample from the same population at a time. Suppose, we want to simulate an experiment when we take a random sample of 20 men, and measure their systolic blood pressure.

Use 3 different Samples, and compare the data measured in the different samples. We know that for the population of males systolic blood pressure is approximately normally distributed with Mean 130 and Standard Deviation of 20 millimeters of Mercury. "

From the lecture:

"In this tutorial we will see a useful technique for Simulation Studies. This technique is good to study the variation of different Sample Statistics even in the case when the theoretical approach is quite complex."