MA121: Introduction to Statistics

Read this brief introduction to the field of statistics and some relevant examples of how statistics can lend credibility to making arguments. Complete the practice questions in these sections.

Read these sections and complete the questions at the end of each section. Here, we introduce descriptive statistics using examples and discuss the difference between descriptive and inferential statistics. We also talk about samples and populations, explain how you can identify biased samples, and define differential statistics.

Read section 1 from chapter 1 to further enhance your understanding of the elements of descriptive and inferential statistics. This section will introduce some of the key concepts in statistics and has numerous exercise and examples. Complete the odd-numbered exercises before checking the answers.

Read these sections and complete the questions at the end of each section. This section introduces several types of data and their distinguishing features. You will learn about independent and dependent variables and how common data can be coded and collected.

This section talks about how data can be presented. Attempt the exercises and check your answers.

Read these sections and complete the questions at the end of each section. First, we'll look at the available methods to portray distributions of quantitative variables. Then, we'll introduce the stem and leaf plot and how to capture the frequency of your data. We'll also discuss box plots for the purpose of identifying outliers and for comparing distributions and bar charts for quantitative variables. Finally, we'll talk about line graphs, which are based on bar graphs.

This section elaborates on how to describe data. In particular, you will learn about the relative frequency histogram. Complete the exercises and check your answers.

Read these sections and complete the questions at the end of each section. First, we will define central tendency and introduce mean, median, and mode. We will then elaborate on median and mean and discusses their strengths and weaknesses in measuring central tendency. Finally, we'll address variability, range, interquartile range, variance, and the standard deviation. 

This section elaborates on mean, median, and mode at the population level and sample level. This section also contains many interesting examples of range, variance, and standard deviation. Complete the exercises and check your answers.

Watch this video series, which begins with a discussion on descriptive statistics and inferential statistics and then talks about mean, median, and mode, as well as sample variance.

This section discusses percentiles, which are useful for describing relative standings of observations in a dataset.

Watch this tutorial to learn how to create the scatter plot for bivariate data using two variables, x and y.

This section introduces Pearson's correlation and explains what the typical values represent. It then elaborates on the properties of r, particularly that it is invariant under linear transformation. Finally, it introduces several formulas we can use to compute Pearson's correlation.

First, we will discuss experiments where outcomes are equally likely to occur and the frequency approach to assigning probabilities. Then, we will focus on the concept of events and touch on the issue of conditional probability.

Read this section about basic concepts of probability, including spaces, and events. This section discusses set operations using Venn diagrams, including complements, intersections, and unions. Finally, it introduces conditional probability and talks about independent events.

This section introduces formulas for combinations and permutations, which are helpful in computing probabilities.

Watch these videos, which introduce Venn diagrams in the context of playing cards and discuss the addition rule for probability.

This section first defines discrete and continuous random variables. Then, it introduces the distributions for discrete random variables. It also talks about the mean and variance calculations.

Watch these videos on binomial distributions. The first explains how to compute the mean of a binomial distribution. The next two videos introduce binomial probabilities and show how to graph them. The remaining videos elaborate on binomial distribution in the context of basketball examples.

First, we will talk about binomial probabilities, how to compute their cumulatives, and the mean and standard deviation. Then, we will introduce the Poisson probability formula, define multinomial outcomes, and discuss how to compute probabilities by using the multinomial distribution.

This section talks about the standard normal curve and how to compute certain areas underneath the curve. This section also contains numerous exercises and examples.

First, this section talks about the history of the normal distribution and the central limit theorem and the relation of normal distributions to errors. Then, it discusses how to compute the area under the normal curve. It then moves on to the normal distribution, the area under the standard normal curve, and how to translate from non-standard normal to standard normal. Finally, it addresses how to compute (cumulative) binomial probabilities using normal approximations.

Watch this video on the normal distribution. It introduces the normal distribution and its density curve and explains how to read the areas underneath the normal curve. It also touches on the central limit behavior.

This section introduces sampling distribution using a concrete, discrete example, followed by a continuous example. This section also discusses sampling distributions' relationship to inferential statistics.

Use the information provided on the demonstration pages and interact with the various simulations.

If you have not done so already, you will need to download install the free Wolfram CDF Player™. If using Chrome as your browser, you will also need to download the CDF files from the pages linked to above, and run them through the CDF Player on your desktop. Other browsers will allow you to interact with the demonstrations directly on the webpage.

First, this section discusses the mean and variance of the sampling distribution of the mean. It also shows how central limit theorem can help to approximate the corresponding sampling distributions. Then, it talks about the properties of the sampling distribution for differences between means by giving the formulas of both mean and variance for the sampling distribution. Using the central limit theorem, it also talks about how to compute the probability of a difference between means being beyond a specified value.

This section gives several concrete examples of calculating the exact distributions of the sample mean. The corresponding means and standard deviations are computed for demonstration based on these distributions. Next, it discusses sampling distributions of sample means when the sample size is large. It also considers the case when the population is normal. Finally, it uses the central limit theorem for large sample approximations.

Watch these videos, which discuss sampling distributions.

Watch this video on determining the standard deviation.

First, we'll discuss the basic concepts of sample statistics and population parameters. Then, we'll talk about the degree of freedom, which is the number of independent pieces of information that a point estimate is based on. Finally, we will talk about variance, which depends on the degrees of freedom.

This section discusses two important characteristics used as point estimates of parameters: bias and sampling variability. Bias refers to whether an estimator tends to over or underestimate the parameter. Sampling variability refers to how much the estimate varies from sample to sample.

This section explains the need for confidence intervals and why a confidence interval is not the probability the interval contains the parameter. Then, it discusses how to compute a confidence interval on the mean when sigma is unknown and needs to be estimated. It also explains when to use t-distribution or a normal distribution. Next, it covers the difference between the shape of the t distribution and the normal distribution and how this difference is affected by degrees of freedom. Finally, it explains the procedure to compute a confidence interval on the difference between means.

This demonstration provided here is a supplement to the previous section.

Read the instructions and watch the video to see how the degrees of freedom affect the difference between t and normal distributions.

This demonstration is a supplement to the previous materials.

Watch these videos, which discuss confidence intervals.

First, this section discusses whether rejection of the null hypothesis should be an all-or-none proposition. Then, it discusses how to interpret non-significant results; for example, it explains why the null hypothesis should not be accepted or should be accepted with caution. It also describes how a non-significant result can increase confidence that the null hypothesis is false.

Watch these videos on hypothesis testing.

This section shows how to test the null hypothesis that the population mean is equal to some hypothesized value, using a very concrete example. In this example, all the main elements of hypothesis testing come in to play a role.

This section talks about using the central limit theorem to test a population mean when the sample size is large. It also addresses how to interpret the test results in the application background. Then, it discusses testing a population mean when the sample size is small, outlines a five-step testing procedure, and illustrates the procedure with an example. Study the example carefully and complete the relevant exercises and applications. Finally, it talks about large sample tests for a population proportion. The critical value and p-value approach are introduced based on a standardized test statistic.

This section covers how to test for differences between means from two separate groups of subjects and gives an example of opinions on animal research. The detailed testing procedure is carried out using the standard steps in hypothesis testing.

Watch these videos on the difference of means.

Watch these videos, which discuss comparing population proportions. While these videos are optional, studying these topics may help you if you are interested in taking the credit-aligned exam that is linked with this course.

This section defines simple linear regression, uses scatter plots to reveal linear patterns, and talks about prediction error. It also discusses how to compute regression line by minimizing squared errors.

Read these sections on linear regression. Linear regression, the simplest form of regression, is used to obtain a linear relationship between two variables.

Read this discussion on linear correlation. You will learn what the linear correlation coefficient is, how to compute it, and what it tells us about the relationship between two variables x and y.

This section discusses the sums of squares, including partitioning sum of squares into sums of squares predicted and sum of squares error.

Watch these videos, which discuss the regression line.

This section discusses how to compute the standard error of the estimate based on errors of prediction as well as how to compute the standard error of the estimate based on a sample.

This section starts with assumptions on the errors that are necessary for statistical inference. Then, it gives an example of a significance test for the slope. Finally, it talks about constructing confidence intervals for the slope and closes with a significance test for the correlation.

This section further details two types of inferences on the slope parameter, considering both confidence intervals and hypothesis testing.

This section discusses the notion of influence and describes what makes a point influential. It introduces the concepts of leverage and distance, which are useful to detect influential observations.

This section explains linear regression, from presenting the data to using scatter plots to identify the linear pattern. It then fits a linear model using least squares estimation and addresses statistical inferences on correlation coefficient and slope parameter.

Watch these videos, which discuss each of the steps in ANOVA. While these videos are optional, studying ANOVA may help you if you are interested in taking the credit-aligned exam that is linked with this course.

Read this chapter and complete the questions at the end of each section. While these sections are optional, studying ANOVA may help you if you are interested in taking the Saylor Direct Credit exam for this course.