|
The following is a help on statistics tutorial. This tutorial will provide you with numerous concepts based upon statistics like probability distributions, sampling distributions, statistical inference estimation and testing, statistical quality control, design of sample survey, design of experiments, multivariate analysis, regression etc.
What do You Mean by Statistics?
Statistics involves the analysis of the frequency of past events. Statistics is primarily an applied branch of mathematics, which tries to make sense of observations in the real world. Statistical theory enables us to measure the extent to which our world is ideal.
The Statistician Turns This Around:
1. Rules ← data: Given only the data, try to guess what the rules were. That is, some probability model controlled what data came out, and the best we can do is guess or approximate what that model was. We might guess wrong; we might refine our guess as we get more data.
2. Statistics is about looking backward.
3. Statistics is an art. It uses mathematical methods, but it is more than math.
4. Once we make our best statistical guess about what the probability model is (what the rules are), based on looking backward, we can then use that probability model to predict the future. (This is, in part, why I say that probability doesn't need statistics, but statistics uses probability.)
Example:
Suppose you are given a list of heads and tails. You, as the statistician, are in the following situation:
You do not know ahead of time that the coin is fair. Maybe you've been hired to decide whether the coin is fair (or, more generally, whether a gambling house is committing fraud).
You may not even know ahead of time whether the data come from a coin-flipping experiment at all.
Suppose the data are three heads. Your first guess might be that a fair coin is being flipped, and these data don't contradict that hypothesis. Based on these data, you might hypothesize that the rules governing the experiment are that of a fair coin: your probability model for predicting the future is that heads and tails each occur with 50% likelihood.
If there are ten heads in a row, though, or twenty, then you might start to reject that hypothesis and replace it with the hypothesis that the coin has heads on both sides. Then you'd predict that the next toss will certainly be heads: your new probability model for predicting the future is that heads occur with 100% likelihood, and tails occur with 0% likelihood.
If the data are "heads, tails, heads, tails, heads, tails", then again, your first fair-coin hypothesis seems plausible. If on the other hand you have heads alternating with tails not three pairs but 50 pairs in a row, then you reject that model. It begins to sound like the coin is not being flipped in the air, but rather is being flipped with a spatula. Your new probability model is that if the previous result was tails or heads, then the next result is heads or tails, respectively, with 100% likelihood.
How Helpful is This Tutorial:
The Statistics tutorial will help you to use the right probability distribution i.e. the appropriate probability distribution viz. normal, binomial, Poisson, uniform, t, etc. for analysis purpose. It will help you in estimating population means and proportions, based on sample data. Also, margin of error and confidence levels and intervals can also be determined with the help of this tutorial. In statistical testing the hypotheses about means and proportions is also covered in the tutorial. The sample design that yields maximum precision for minimum cost and many other topics under statistics is covered here in the statistics tutorial.
The Statistics tutorial will prove helpful for both who want to gain their knowledge about statistics and also the students who are new to statistics. The analytical tools like statistical tables or calculators are also provided. Apart, from these sample problems based on statistics are also there for you. And lastly, you can also get online statistics help.
|
