MMW Chap 3 Data Management Test Statistics With Voice

Statistics Applied to Research

• Making informed decisions often relies on data in business, education, health, or social sciences.
• Statistical tests help determine if data is truly significant.
• Covers parametric tests, including t-tests, ANOVA, correlation, and regression.
• Tools like Excel can be used to analyze and interpret results.

Learning Objectives

• Differentiate between independent and dependent samples.
• Identify appropriate statistical tests.
• Formulate null and alternative hypotheses for t-tests, ANOVA, and correlation.
• Perform parametric tests using Excel.
• Interpret statistical results using p-values.
• Evaluate whether assumptions for parametric tests are met.

Summary of Statistical Tests and Uses

Describing One Group

• Ratio/Interval Data (Normal Distribution):
  • Test statistics: Mean and standard deviation.
• Ratio/Interval Data (Not Normal Distribution):
  • Test statistics: Median, interquartile range, and range.
• Ordinal Data (Not Normal Distribution):
  • Test statistics: Median, interquartile range, and range.
• Nominal Data (Not Normal Distribution):
  • Test statistics: Proportion or frequency (percentage).

Example:

• Assessing schools in the Philippines (public or private) using frequency and percentage.
• Number of enrollment (small, medium, large) using the mean.

Comparing One Group to a Hypothetical Value

• Ratio/Interval Data (Normal Distribution):
  • Test statistic: One sample t-test.
• Ratio/Interval Data/Ordinal (Not Normal Distribution):
  • Nonparametric test: Wilcoxon test.
• Nominal Data (Not Normal Distribution):
  • Test statistic: Chi-square test (goodness of fit).

Example:

• Testing the claim that the average weight of a student population is greater than 140 using the weight data of 10 students.

Comparing Differences Between Two Independent Groups (Unpaired Groups)

• Dependent variable: Ratio/interval, ordinal, nominal.
• Independent variable: Two categorical independent groups.
  • Normal Distribution: Independent sample t-test.
  • Not Normal Distribution (Ratio/Interval): Mann-Whitney U test.
  • Ordinal (Not Normal Distribution): Mann-Whitney U test.
  • Nominal (Not Normal Distribution): Fisher's exact test.

Example

• Do standardized test scores (mathematics, reading, writing) differ between students who failed and passed the final exam?
  • Dependent variable: Scores for mathematics, reading, and writing.
  • Independent variable: Students who failed and passed.

Comparing Differences Between Two Related Groups (Paired Groups)

• Dependent variable: Ratio/interval, ordinal, nominal.
• Independent variable: Two categorical related groups.
  • Normal Distribution: Paired sample t-test.
  • Not Normal Distribution (Ratio/Interval/Ordinal): Wilcoxon signed-rank test.
  • Nominal (Not Normal Distribution): McNemar's test.

Example:

• Is there a significant difference in the average number of words recalled before and after training?
  • Dependent variable: Number of words recalled.
  • Independent variable: Before and after training.

Comparing Differences Between Means of Two or More Independent Groups

• Dependent variable: Ratio/interval, ordinal, nominal.
• Independent variable: Two or more categorical independent groups.
  • Normal Distribution: One-way ANOVA.
  • Not Normal Distribution (Ratio/Interval/Ordinal): Kruskal-Wallis test.
  • Nominal (Not Normal Distribution): Chi-square test.

Example

• Is there a significant difference in parental involvement in children's education based on civil status (single, married, separated, widowed)?
  • Dependent variable: Rating for home-related and school-related support.
  • Independent variable: Civil status.

Measuring Association Between Two Variables

• Dependent variable: Ratio/interval, ordinal, nominal.
• Independent variable: Ratio/interval, ordinal, nominal.
  • Normal Distribution: Pearson correlation.
  • Not Normal Distribution: Spearman correlation.
  • Both Nominal: Contingency coefficients or Chi-square test.

Example:

• Is there a significant relationship between the number of hours spent studying and final grades?
  • Dependent variable: Final grades.
  • Independent variable: Number of hours spent studying.

Predicting or Estimating the Value of a Variable

• Dependent variable: Ratio/interval, ordinal, nominal.
• Independent variable: Nominal, ordinal, interval, or ratio.
  • Normal Distribution: Linear regression.
  • Ordinal Dependent: Ordinal regression.
  • Nominal Dependent: Logistic regression.

Example:

• Determine significant factors affecting the demand for books.
  • Dependent variable: Number of books purchased.
  • Independent variables: Price, annual budget, cost of unused books.

Statistics Applied to Research

• Parametric tests assume underlying statistical distributions (normal distribution).
• Several conditions of validity must be met.
• Applied to data in ratio and interval scales.

Inference About Two Means

• Determine if data comes from independent or dependent samples.
• Independent sampling: Individuals selected for one sample do not dictate individuals in another sample.
• Dependent sampling: Individuals selected in one sample determine individuals in the other sample.

Dependent Sample t-test (Paired t-test)

• Compares means of two related groups.
  • Assumptions:
    • Dependent variable measured at interval or ratio level.
    • Independent variable consists of two categorical related groups.
    • No significant outliers.
    • Differences in dependent variable between groups are approximately normally distributed.

Example:

• A teacher wants to know if a new learning program increases the number of correctly remembered words. 10 subjects learn a list of 50 words with a recall test. Subjects are then instructed on how to use the learning program. Then learn another list of 50 words and the test is administered again.

Steps in Hypothesis Testing

1. State the null and alternative hypotheses.
2. Set the level of significance (alpha).
3. Determine the test distribution to use.
4. Calculate the test statistic or p-value.
5. Make a statistical decision.
6. Draw a conclusion.

Example (Continued)

• Null Hypothesis: The new learning program will not increase the number of correctly remembered words.
  $H<em>0: \mu</em>d \leq 0$
• Alternative Hypothesis: The new learning program will increase the number of correctly remembered words.
  H1: \mud > 0
• Alpha level: 0.05
• Dependent variable: Number of correctly remembered words.
• Independent variable: Treatment before and after
• Test: Dependent sample t-test

*Using Excel to calculate the computed/p value.

• If p-value $\leq$ alpha, reject the null hypothesis.
• If p-value > alpha, fail to reject the null hypothesis.

Presentation of results:

• T Value: Negative 2.913
• P Value: Highlight Three Decimal Places (Depends)

Independent Sample t-test

• Evaluate/compare the mean difference between two independent populations using data taken from the groups.
  • Assumptions:
    • Dependent variable is continuous on a continuous scale measure at interval or ratio level.
    • Independent variable has two groups (categorical, independent groups.)
    • No outliers.
    • Dependent variables should be approximately normal for each group of independent variable.
    • There needs to be homogeneity of variances.

Example:

• Researchers divide 18 people into two groups to verify if the different styles of text(visual manual and unimodal instruction) makes a difference in learning a software comprehension program. Text is given. 2 tests. 1 is Visual and the other is Textual style.

• Visual Column and Textual Column

• State null and alternative hypotheses:

  • Null: There is no significance between scores of the learning computer program given the different textual and visual way.
    $H<em>0: \mu</em>1 = \mu_2$

  • Alternative: There is a significance between scores of the learning computer program given the different textual and visual way.
    $H<em>A: \mu</em>1 \neq \mu_2$

  • Alpha of 0.05

• Dependent Variable = Scores

• Independent Variable = Styles of Text.

• F-Test will measure if variances are equal or unequal.

*Using the P approach in excel

• Reject the alternatives and accept the null or failed to reject the null with p-value > than alpha
• Homogeneity and equal variables are assumed

T Tests

• Measure if it’s assuming equal variables or if it’s un equal

• 2 Tailed Measure when equal and when not, the measure will be greater (lumabas) or not to one tailed test

• Make Statistical Difference by using data

Presentation of results:

One Way Analysis of Variance (ANOVA)

• ANOVA: Measures if the K (of 3 or more populations is the same or not)
  $H<em>0: \mu</em>1 = \mu<em>2 = \mu</em>k$
  $H<em>A: \mu</em>I$

  Alternative, at least one of the population means is different from the other
  Assumptions:

• Dependent valuable should be measured at the interval or in ratio level continuous

• Independent should have more than 2 categorical independent groups.

• That that data can be outliers.

• Dependent should be approximately following normal distribution for each category of the independent variable

• Needs to be homogeneity of variables
  Researchers wanted To see math scores from various cities students taking secondary school and then randomly sampled 8 test takers 1 in make Manila Keson city to test score exam results can the researchers confirm that the distribution exam different from each city given a 0.1 significance

• To see if variance is not measuring variable click data data analysis F test samples variable highlighting moving dollar and so on since you said equal what not use 1 tail since he want the equal not so have to have 2. In the value is more compared to the value in hypothesis reject reject know since failed reject know in this equals now if the if can see between cases between city1 and variables data and so on and since data this data more 9196
  *Click to column labels for that is 0100 rejected value reject alternative test value value since and the there the means in groups to see the numbers and see since hypothesis can since it since 0. With scores

Presentation of Results

• indicator of test show means math is different with math scores different for is it and then since there this there mathematics and there from reject that math is or

Pearson Product Moment Correlation

• Pearson R is a measurement of the strength in linear correlation association between 2 variables and has been called R to find it you need to do correlate significance or the significant relationships between variables test to to variable will in to from direct from From close strong from from from As is so relationship For so relationships variables. What
  An also also so for analysis the ratio relation. So So. So.

Assumptions

• Two measured to also the to know Also equals close also that is science There about
  State to what data in to There intake to hypothesis there is So know test there intake the P we intake equal will Then. So So we is and
  Final. Variable test Intake And correlation for and the is. With 22 SQRT the value After parenthesis comma equals so test the equals equals close a with which And is and strong intake intake strong not presentation is

Regression Analysis

• Most primarily to do that and in to is relationship There Then regression