Child Development 133 
Research Methods in Human Development

Sections 04, 68, & 69
Hembree           Spring, 2011


Analyzing Data/Inferential Statistics

Be sure to print out handouts for:


I. Introduction

A. Conceptual perspective - what are doing when we analyze quantitative data?

1.     Computing statistic that represents the data (e.g., mean differences)




2.      Results (e.g., mean differences) can be due to IV, confound, or error





3.   Comparing the results (e.g., mean differences) we obtain with what we might expect by chance.





4. If determined unlikely to have occurred by chance, then infer results (e.g., mean differences) are "real", that they are "statistically significant"



B. The role of probability, chance and error

1. Use principles of probability (likelihood) to make decisions about data



2. Could these results have occurred by chance?

e.g.,  consider the mean scores of two groups  12.0 and 13.0. Are they really different? Or did they different simply by chance?



All things being equal, we are more convinced when we see larger differences between means.  Why?





All things being equal, we are more convinced when standard deviations are low. Why?





All things being equal, we are more convinced when numbers are participants are high. Why?




II. Hypothesis testing

A. Null hypothesis/Experimental hypothesis




B.  Decision: Fail to reject vs. reject




  • reject null = statistical significance





C.     Making decisions and making mistakes

Possible outcomes:






Reject Null

Fail to reject Null




What is true in

the population?


Null is false






Type II error



Null is true


Type I error






1.      Type I error 



2.      Type II error




Which error is worse?




3.      Power




Power is increased by:

  •  Reducing error (as measured by s)



  •  Increasing # of subjects



  •  Increasing the effect size



III. Inferential Statistics

A. What is meant by inference?




B.  t-test

  • used to test association between categorical variable (group membership) and continuous variable (e.g., mean differences in performance)

t = association/lack of association

1.      calculate means for each group

2.      calculate variance for each group; calculate pooled variance

3.      compute t

4.      find critical t, given specified alpha and degrees of freedom

5.      compare obtained t with critical t; make decision




C. Chi-square (handout)

  •  Used to test the association between two nominal (categorical) variables


  1. Calculate marginal frequencies

  1. Calculate expected values for each cell

  1. Calculate chi-square

  2. Find critical chi-square, given alpha and degrees of freedom

  3. Compare chi-square with critical chi-square; make decision




  D. Pearson r (handout)

  • used to test association between two continuous variables










Send problems, comments or suggestions to:

California State University, Sacramento
College of Education
Department of Child Development

Updated: January, 2011