Leading Questions
    • What do you think is the main difference 
     between descriptive statistics and 
     inferential statistics?
    • What is population?
    • What is a sample?
    • What is hypothesis testing?
        The Logics of Inferential 
        Statistics
    • Inferential statistics are used to gain a better 
     understanding of the nature of the relationship 
     between two or more variables (e.g., linear or 
     causal-like relationships).
    • A population = the totality of the people in 
     which they are interested)
    • A sample is those drawn from that population 
     (i.e., a selection of people from the population)
    • A parameter is a characteristic of a population
    • A statistic is a characteristic of a sample that 
     will be used to infer a parameter. 
        Hypothesis and Inferential 
        Statistics
    • Inferential statistics are employed to estimate 
      the parameter of the target population.
    • A null hypothesis is a statistical statement that 
      there is no relationship between two variables.
    • Inferential statistics are used to test the null 
      hypothesis and aim to evaluate whether the null 
      hypothesis can be rejected.
    • When the null hypothesis is rejected, researchers 
      can accept an alternative hypothesis which states 
      that there is a relationship.
                 Hypothesis Testing
        • Hypothesis testing is a statistical approach to 
           investigating how well quantitative data support 
           a hypothesis.
        • The null hypothesis (H ) is basically the 
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           prediction that there is no relationship between 
           two variables, or no difference between two or 
           more groups of learners.
        • When the data do not support the null 
           hypothesis, the researchers will accept the 
           hypothesis called the alternative hypothesis 
           (H1) which is logically the opposite of the null 
           hypothesis. 
        Probability Value
    • In order to reject the null hypothesis, 
     researchers must set a probability value 
     (i.e., p-value).
    • The probability value is directly set for 
     testing the null hypothesis, not for the 
     alternative hypothesis.
    • In language learning research, for example, 
     researchers usually set a probability value to 
     be less than 0.05 (p < 0.05) or sometimes 
     equal to or less than 0.05 (p ≤ 0.05).