The researcher is similar to the prosecuting attorney is the sense that the researcher brings the null hypothesis “to trial” when she believes there is probability strong evidence against the null.

• Just as the prosecutor usually believes that the person on trial is not innocent, the researcher usually believes that the null hypothesis is not true.
• In the court system the jury must assume (by law) that the person is innocent until the evidence clearly calls this assumption into question; analogously, in hypothesis testing the researcher must assume (in order to use hypothesis testing) that the null hypothesis is true until the evidence calls this assumption into question.

In this case the unstandardized multiple regression coefficient is interpreted as the predicted change in Y (i.e., the DV) given a one unit change in X (i.e., the IV) while controlling for the other independent variables included in the equation.

• The regression coefficient in multiple regression is called the partial regression coefficient because the effects of the other independent variables have been statistically removed or taken out (“partialled out”) of the relationship.
• If the standardized partial regression coefficient is being used, the coefficients can be compared for an indicator of the relative importance of the independent variables (i.e., the coefficient with the largest absolute value is the most important variable, the second is the second most important, and so on.)

The basic or unstandardized regression coefficient is interpreted as the predicted change in Y (i.e., the DV) given a one unit change in X (i.e., the IV). It is in the same units as the dependent variable.

• Note that there is another form of the regression coefficient that is important: the standardized regression coefficient. The standardized coefficient varies from –1.00 to +1.00 just like a simple correlation coefficient;
• If the regression coefficient is in standardized units, then in simple regression the regression coefficient is the same thing as the correlation coefficient.

In each of these, the null hypothesis says there is no relationship and the alternative hypothesis says that there is a relationship.

1. In this case the null hypothesis says that the two population means (i.e., and  ) are equal; the alternative hypothesis says that they are not equal.
2. In this case the null hypothesis says that all of the population means are equal; the alternative hypothesis says that at least two of the means are not equal.
3. In this case the null hypothesis says that the population correlation (i.e., ) is zero; the alternative hypothesis says that it is not equal to zero.
4. In this case the null hypothesis says that the population regression coefficient () is zero, and the alternative says that it is not equal to zero.

In hypothesis testing there are two possible errors we can make: Type I and Type II errors.

• A Type I error occurs when your reject a true null hypothesis (remember that when the null hypothesis is true you hope to retain it).
• A Type II error occurs when you fail to reject a false null hypothesis (remember that when the null hypothesis is false you hope to reject it).
• The best way to allow yourself to set a low alpha level (i.e., to have a small chance of making a Type I error) and to have a good chance of rejecting the null when it is false (i.e., to have a small chance of making a Type II error) is to increase the sample size.
• The key in hypothesis testing is to use a large sample in your research study rather than a small sample!

If you do reject your null hypothesis, then it is also essential that you determine whether the size of the relationship is practically significant

It has become part of the statistical hypothesis testing culture.

• It is a longstanding convention.
• It reflects a concern over making type I errors (i.e., wanting to avoid the situation where you reject the null when it is true, that is, wanting to avoid “false positive” errors).
• If you set the significance level at .05, then you will only reject a true null hypothesis 5% or the time (i.e., you will only make a type I error 5% of the time) in the long run.

This is an opinion question.

• Point estimation is nice because it provides an exact point estimate of the population value. It provides you with the single best guess of the value of the population parameter.
•  Interval estimation is nice because it allows you to make statements of confidence that an interval will include the true population value.

The two general rules are

• 1) If the mean is less than the median, the data are skewed to the left, and
• 2) If the mean is greater than the median, the data are skewed to the right.

Therefore, if the mean is much greater than the median the data are probably skewed to the right.

The problem with using a point estimate is that although it is the single best guess you can make about the value of a population parameter, it is also usually wrong.

• A major advantage of using interval estimation is that you provide a range of values with a known probability of capturing the population parameter (e.g., if you obtain from SPSS a 95% confidence interval you can claim to have 95% confidence that it will include the true population parameter.
• An interval estimate (i.e., confidence intervals) also helps one to not be so confident that the population value is exactly equal to the single point estimate. That is, it makes us more careful in how we interpret our data and helps keep us in proper perspective.
• Actually, perhaps the best thing of all to do is to provide both the point estimate and the interval estimate. For example, our best estimate of the population mean is the value $32,640 (the point estimate) and our 95% confidence interval is $30,913.71 to $34,366.29.
• By the way, note that the bigger your sample size, the more narrow the confidence interval will be.
• If you want narrow (i.e., very precise) confidence intervals, then remember to include a lot of participants in your research study.

A scatterplot (also called a scatter graph). It is traditional to let the X axis (the horizontal axis) represent the independent/predictor variable and let the Y axis (the vertical axis) represent the dependent/outcome variable.