Choosing and using your statistic

Steps of hypothesis testing 1. Establish the null hypothesis, H 0. 2.Establish the alternate hypothesis: H 1. 3.Decide your level of “confidence” 4.Use the level of significance and the alternate hypothesis to determine the critical region. 5.Find the critical values of Z that form the boundaries of the critical region(s). 6.Use the sample evidence to draw a conclusion regarding whether or not to reject the null hypothesis. The sample evidence is the data you collect—the mean and standard deviations in your data

The null hypothesis For an experimental design – There will be no change in the DV that can be predicted by the IV For a naturalistic or survey research design – There will be no relationship between the X and Y variables

The alternate hypothesis For an experimental design – The DV will change in response to change in the IV For a naturalistic or survey research design – The variables X and Y will be related

Your level of confidence? Should be 95% Meaning your P value or alpha will be set at.05

Which statistical test will you use? It depends on the question It depends on the types of numerical variables you have and how they are distributed – Continuous (or quasi continuous) – Categorical – Nominal Nominal variables aren’t actually numerical, but can be represented by numbers and used in certain statistical manipulations

What types of variables do you have? Continuous (or quasi continuous) – Variables that are measured on a “scale” – In which the responses show some variability Examples – Questionnaires that yield scaled values E.g. happiness on a scale of 0-20 – Measurable amounts Amount of food eaten in ounces

Distribution There should be some variability It doesn’t have to be normal You will need to look at the distributions We will do that in SPSS

What if your variable isn’t distributed with variation? It may influence the types of analysis you can do and the type of test you choose.

What types of variables do you have? Rank ordered categorical – Can be assigned numbers, but aren’t as numerically precise as “continuous” – The difference between these and “continuous” variables can be murky – The key is if you have, say, a 4-point rank order variable (not happy, sort of happy, happy, really happy) will it have a distribution?

What types of variables do you have? Nominal – Not rank ordered – May be more than two categories Though for your purposes that will probably be unlikely Examples – Yes/no questions – Gender

What types of tests/statistics will you use? Descriptives – Means, SD or Frequencies – Range – Refusal (unlikely to happen) – Drop out (if that happens) – Missing (if people don’t complete measures)

What types of tests/statistics… Descriptives – Testing for outliers and distributions – Cohen’s kappa (interrater reliability) Do observers agree – Cronbach’s alpha (internal consistency reliability) Do respondents understand your questions to assess the same construct? – Test-retest reliability Do respondents maintain similar rank order on your survey over time?

Types of tests/statistics… Some descriptives may require inferential statistics – T-tests To see if there were differences in missing data E.g. if you have two groups, people with missing data and those without, did they differ by age, income, etc? – MANOVA To see if groups differ on multiple baseline scores E.g. 3 different educational treatments and reading, math and science scores You won’t be likely to need this

What inferential statistics? Comparing differences between groups – T tests – Analysis of Variance – Multiple analysis of Variance – Analysis of covariance Relations among continuous or rank ordered variables – Correlation, partial correlation – regression

T-tests Difference in means between two groups Predictor should be 2 levels Are the groups dependent or independent? – Matched pairs, repeated measures Outcome should be continuous or rank ordered – If outcome is binomial use chi-square – E.g. male/female by drug use yes/no Statistic is T

Analysis of Variance (one way) Differences between two or more groups – You may have only two groups but use ANOVA because you can do more with it than a T-test Predictor should be nominal or categorical Outcome should be continuous or rank ordered Within subjects (repeated measures designs) – You won’t be using this (why?) – But its important to be aware of

Analysis of Variance (one-way) Between subjects Looking for differences in variation across groups Predictors nominal or categorical Outcomes continuous or rank ordered Statistic is F (ominibus) Tells you if there is any difference at all “Post hoc” tests can tell you which groups are actually different

Analysis of Variance (two-way) Between subjects Looking for differences in variation across groups Predictors should be nominal or categorical Outcome variable should continous You can look at “main effects” and “interactions”

Two way ANOVA example Outcome: Depression scores Predictors – treatment type: TAU, CBT, Pet therapy – Gender: Male, female You can examine main effects – Did treatment type influence depression – Did gender influence depression Interactions – Did males/females have different outcomes by treatment types?

Analysis of Covariance Like ANOVA, but allows you to “control” for the influence of another predictor It is often used with repeated measures to control for “baseline” scores But can be used with any predictor variable you want to control for It can control for “continuous” predictor variables You can use this instead of a T test if you only have two groups and want to control for a variable

Analysis of Covariance, example Outcome: height in inches Predictors: – Exercise program (none, some, a lot) – Gender (male/female) Control variable? – Calories consumed

Relationships between variables Correlation Partial correlation Regression

Correlation The relationship between two continuous variables – May end up being the relationship between rank ordered variables – A different type of correlation may be used for this (Spearman), but you will probably use Pearson. They are often the same, anyway

Correlation Varies between -1 and 1. Is referred to as R Null hypothesis is usually R=0 Positive correlation means that higher scores on one variable are associated higher scores on the other Negative correlation: higher scores on one associated with lower scores on the other

Partial correlation How two variables are related, controlling for the influence of a third variable The technique “partials out” the influence of the third variable E.g. how are happiness and exercise correlated after partialing out the influence of age on both variables?

Regression A technique you are very likely to use if you go on in psychology Frequently employed in naturalistic research There are a number of types of regression We’ll be using multiple regression Predictors: continuous or rank ordered variables – And also sometimes nominal variables Outcome: continuous or rank ordered variables

Regression What does it tell us? The contribution each variable makes in predicting the outcome The combined contribution the variables together make The amount of “movement” in Y you get from “movement” in X Regression is related to correlation

Regression: Example Outcome variable: marital happiness scale Predictor variables: income, gender, education, neuroticism scale scores We can see how much each one contributes to the prediction of marital happiness as measured by the scale

Rank Ordered Variable Distribution In practice you are likely to treat this analytically the same way you would treat a continuous variable