Scopes and Methods Final Exam prep

Logistic Regression

Nonlinear regression model that relates a set of explanatory variables to a dichotomous dependent variable.

Logistic Regression is used when?

When the dependent variable is categorical and binary

Linear Regression predicted Y can Exceed what range?

0 & 1

Logistic Regression predicted y lies within what range?

0 & 1

P =

Occurrences/Chances

Odds =

Occurances/Non-occurances

Odds =

Ratio of the probability of an event and probability of the event not occurring.

Logged odds

Expresses a number as an exponent of a constant or base

Correlation Coefficient - Pearson’s r

-1 to 1

If something’s correlation coefficient is 1 it is?

Perfectly correlated and positive

If something’s correlation coefficient is -1 it is?

Perfectly correlated and negative

If something’s correlation coefficient is 0 it is?

Unrelated

Bivariate Regression conditions

Gives effect of one independent variable on a dependent variable

Gives magnitude and direction

Magnitude

How much change we see on the dependent variable with the independent present

Multiple regression

Gives effect of multiple independent variables on the dependent variables while controlling for the effects of the other independents.

Gives effect of each independent variable while considering the effect of other independents.

Gives the effect of the optimal combination of the independent variables on the dependent variable

Assertion of causality comes when

Temporal sequence

Relationships between variables

No plausible alternate explanations

Multicollinearity in multiple regression models

Situation in which independent variables are so strongly related that it is difficult to estimate the partial effect of each independent variable on the dependent variable

Multicollinearity becomes more of a concern as we increase the number on independent variables

Multicollinearity in multiple regression models

The problem is related to the strength or degree of the relationship between the independent variables.

Regression is robust and able to partial shared variance of the independent variable

Expected that the independent variable will be related to some degree

Interaction effect

Occurs when the effect of an independent variable cannot be fairly summarized by a single partial effect

The effect varies depending on the value of another independent variable in the model

Cross-tabulation rules

Interpret by comparing percentages across columns at the same value of the dependent variable

Always calculate percentages of categories of independent variable and never calculate percentage of dependent variable

Type one error occurs when

Rejecting the ho when it should be accepted

Chi Square does which of the following?

Takes into account tabular data

Begins with cross-tabulation

Determines whether the observed dispersal of cases departs significantly from what we would expect to find if the Ho was correct

Degrees of Freedom are

Maximum logically independent values

If the value of Chi Square is greater than the critical value

It is possible to reject the Ho

If the value of Chi Square is less than the critical value

Accept the Ho

If the value of chi square is greater than the critical value

Reject the Ho

Symmetrical

Does not distinguish between dependent and independent variable

Returns the same result no matter which is used

Take on the same value irrespective of which variable is used to explain a relationship

Asymmetrical

Value varies according to which variable is used to explain a relationship

Distinguishes between the dependent and independent

Returns a different result depending on which is used as the dependent and independent variable

Symmetrical measure of association

Gamma 0 to 1 - ordinal level

Asymmetrical

Lambda 0 to 1 nominal level

Cramer’s V 0 to 1

Somer’s d -1 to 1 ordinal level

Proportional Reduction in Error

Bounded by 0 and 1

Lambda and Cramer’s V

PRE for gauging strength of relationships

Distribution

Shows possible values for a variable and how they occur

How the data are distributed across the range of possible values

Central limit theorem

Makes statistical inference possible

Allows us to draw conclusions about a population based on a sample mean

The means from an infinite number of samples drawn from a population are normally distributed and have a mean equal to the population mean. The standard deviation is equal to the population standard deviation divided by the square root of sample size.

1 standard deviation contains what %

68

2 standard deviation contains what %

95

3 standard deviations contain what %

99.7

T distribution was created by

William Gosset

Null hypothesis

Converse of hypothesis we are trying to support

Symbol for hypothesis

Ho

Alternative hypothesis

What we are trying to support

Alternative hypothesis symbol

Ha

Type two error

failing to reject Ho when it be rejected

Levels of statistical significance come from

P Values

The lower the P value the more or less confidence

More

What are the accepted P Values

.10

.05

.01

If p <.10 what confidence level

90% confidence

If p <.05 what confidence level

95% confidence

If p <.01 what confidence level

99% confidence

If p <.001 what confidence level

99% confidence

If p <.000 what confidence level

99% confidence

Why are difference of mean tests used

Used to determine if there is a statistically significant relationship between the means of two variables.

Z test are used for

Population data

T test are used for

Sample data

T tests can be used with

Paired samples

Independent samples

One sample

Interval and Ratio levels of measurement and central tendancy

Mode median mean

Ordinal levels of measurement and measure of central tendancy

Mode median

Nominal levels of measurement and measures of central tendancy

Mode

Measures of dispersion

Range

Deviations from mean

Variance

Standard deviation