Inferential Statistics What are they? When would you use them?
What are inferential statistics? Why learn about inferential statistics? Why use inferential statistics? When are inferential statistics utilized? Which types of inferential statistics are most commonly used and when? What is important for you to know about inferential statistics?
What are inferential statistics? Inferential statistics infer from the sample to the population They determine probability of characteristics of population based on the characteristics of your sample They help assess strength of the relationship between your independent (causal) variables, and you dependent (effect) variables.
Why learn about inferential statistics? BEFORE you use any intervention, you should do some research and determine if there is evidence that it works. (i.e., Does the head start program increase educational performance for low income children) BEFORE you work with any group, you want to base your judgments on research, not on stereotypes (i.e., You may want to know what proportion of Latino boys join gangs?) BEFORE you make recommendations, you want to understand the probabilities of success (i.e., What is the probability that a child will have success in school if they participate in your tutorial program?) Before you continue on with a program/intervention, you want to reassure yourself that this program is worth your time and effort. As you apply for grants, you want to ensure the grantees that you can implement a evidence based program. When making policy recommendations or participating in political advocacy, you want to provide empirical support that your intervention actually works.
Why use inferential statistics? Many top-tiered journals will not publish articles that do NOT use inferential statistics. Allows you to generalize your findings to the larger population. Can determine not just what CAN happen, but what tends to happen in programs like yours. Helps assess strength of the relationship between your independent (causal) variables, and you dependent (effect) variables. Can assess the relative impact of various program inputs on your program outcomes/objectives.
When are inferential statistics utilized? Inferential statistics can only be used under the following conditions. You have a complete list of the members of the population. You draw a random sample from this population Using a pre-established formula, you determine that your sample size is large enough. Can you use inferential statistics even if you data do not meet these criteria? Inferential statistics can help determine strength of relationship within your sample. In other words, you can assess the strength of the impact of your independent variables (program inputs) on your outcomes (program outputs) IF it is very difficult to obtain a population list and/or draw a random sample, then you do the best you can with what you have. In this case, you can use inferential statistics and journals may publish it.
Which types of inferential statistics are most commonly used and when? The following types of inferential statistics are relatively common and relatively easy to interpret. One sample test of difference/one sample hypothesis test Confidence Interval Contingency Tables and Chi Square Statistic T-test or Anova Pearson Correlation Bi-variate Regression Multi-variate Regression
First consider uni-variate statistics. One sample test of difference OR one sample hypothesis test When is it used? To compare responses of program participants on a pre and post test. To determine if implemented program had an impact on one particular outcome. How do you interpret it? If the probability is.05 or less that you will make a mistake in asserting there is a difference between the pre and post-test scores in the population, then you can assert that the program did make a difference on this outcome. In other words, your program is working.
First consider uni-variate statistics. Confidence Interval When is it used? To estimate a value/score in a population based on the score of the participants in your sample. How do you interpret it? A 95% confidence interval indicates you are 95% confident that you can predict/infer the value/score of a population within a specified range based on the value/score of your sample.
Next consider bi-variate statistics. Contingency tables and Chi-Square statistic When are they used? When you have two categorical variables,. AND you want to know if they are related. (i.e., gender and score on outcome measurement). How do you interpret them? The chi-square statistics can be used to determine the strength of the relationship (i.e., Does knowing someone s gender help you predict their outcome score/value). If the probability associated with the chi-square statistics is.05 of less, then you can assert that the independent variable can be used to predict scores on the dependent or outcome variable. You can also use the contingency table to compare the actual scores across the independent variable on the dependent variable or outcome measurement (i.e., compare the number/percent of males who agreed that the program had a positive impact on their lives to the percent of females who agreed.)
Next consider bi-variate statistics. T-test or Anova When is it used? When you have a categorical and continuous variable. And you want to compare mean scores of two or more groups (i.e., you want to compare mean GRP of students you have tutored across race). How do you interpret it? The T-test or F statistic can be used to determine if the groups have significantly different means. If the probability associated with the F statistics is.05 or less then we can assert that there is a difference in the means.
Next consider bi-variate statistics. Pearson Correlation When is it used? When you have a continuous independent variable and a continuous dependent variable. How do you interpret it? When the probability associated with the T statistics is.05 of less then you can assume there is a relationship between the dependent and independent variable. For instance you may want to know if the number of hours participants spend in your program is positively related to their scores on school exams.
Next consider bi-variate statistics. Bi-variate Regression When is it used? When you have a continuous independent variable and a continuous dependent (outcome) variable. For instance, you may want to know if the number of hours participants spend in your program is positively related to their scores on school exams. How do you interpret it? When the probability associated with the F statistic is.05 or less then you can assume there is a relationship between the dependent and the independent variable. * NOTE The Pearson Correlation and Bi-variate regression are very similar.
Finally let us consider multi-variate statistics Elaborated Chi-Square statistic When is it used? When you have more than one independent categorical variable, and one dependent categorical variable. How is it interpreted? You divide one of the independent variables into two groups and then do a chi square for each group (i.e., divide gender into males and females, then do a chi-square of males and one for females. So for females you can do a chisquare of outcome measurement by race, and then do the same for males.)
Multivariate Regression When is it used? Multivariate regression is used you have more than one independent (causal) variable and one dependent (effect or outcome) variable. You not only want to know if you intervention has an impact on the outcome, but you want to know WHICH aspects of your intervention has an impact and/or the relative impact of different aspects of your intervention. How do you interpret it? If the probability associated with the F statistic is.05 of less, then you can If the probability associated with the T statistic for each of the independent variables is.05 or less, then you can assert that independent variable has an impact on the outcome, independent of the other variables. The value of the T statistics can be compared across the independent variables to determine the relative value of each.
What is important for you to know about inferential statistics? You should be able to 1. Read and understand computer printouts 2. Construct tables and graphs from the computer printouts. 3. Interpret and explain these tables and graphs to an audience. 4. Make wise decisions based on valid and accurate data.
What if you NEVER intend to use Inferential Statistics? All of us are consumers of information We can learn about inferential statistics and be wiser consumers of information. We are empowered, and have the tools to determine if the information we are reading is accurate/valid. If you implement programs, you are ethically bound to your participants to be able to accurately measure the outcomes of your intervention. If you use government/foundation funding to implement your programs, then you are responsible for using their monies wisely and efficiently.
Dr. Carol Albrecht USU Extension Specialist carol.albrecht@usu.edu 979-777-2421